Insights By Scott Ernst

Project Autodidact

Project Details: https://insightsbyse.com/projectautodidact/

Scott Ernst Bio: https://insightsbyse.com/aboutscotternst/

Project Contact: InsightsBySE@protonmail.com

Progress Report Scope (S01-M02-D05-AllParts)

Stage 1 of 4: Review of Mathematics, Probability, and Statistics

Module 2 of 3: Statistics, Probability, and Advanced Algebra

Day 5 of 5: Matrices and Determinants

Parts 1 through 10: See below

Summary Of Goals Achieved

1. Reviewed definition, concepts, notation, terminology, components, and properties of matrices
2. Reviewed definition, concepts, notation, terminology, components, properties, rules, and procedures for matrix addition
3. Reviewed definition, concepts, notation, terminology, components, properties, rules, and procedures for matrix subtraction
4. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for performing the tasks and calculations for matrix addition
5. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for performing the tasks and calculations for matrix subtraction
6. Reviewed definition, concepts, notation, terminology, components, and properties of a scalar and scalar matrix
7. Reviewed definition, concepts, notation, terminology, components, and properties of a vector
8. Reviewed definition, concepts, notation, terminology, components, and properties of a covariance matrix
9. Reviewed definition, concepts, notation, terminology, components, and properties of a correlation matrix
10. Reviewed similarities and differences between a covariance and correlation matrix
11. Reviewed definition, concepts, notation, terminology, components, and properties of an eigenvalue and eigenvector
12. Reviewed definition, concepts, notation, terminology, components, and properties of the determinant of a matrix
13. Reviewed definition, concepts, notation, terminology, components, and properties of the dot product (aka scalar product)
14. Reviewed definition, concepts, notation, terminology, components, properties, rules, and procedures for matrix multiplication, including the dot product (aka scalar product)
15. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for performing the tasks and calculations for matrix multiplication, including the dot product (aka scalar product)
16. Reviewed definition, concepts, notation, terminology, components, and properties of the determinant formula
17. Reviewed definition, concepts, notation, terminology, components, and properties of cofactor expansion (aka Laplace expansion)
18. Reviewed definition, concepts, notation, terminology, components, properties, rules, and procedures for calculating the determinant of a 2×2 matrix, 3×3 matrix, 4×4 matrix and higher
19. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for performing the tasks and calculations for calculating determinant of a 2×2 matrix, 3×3 matrix, 4×4 matrix and higher
20. Reviewed definition, concepts, notation, terminology, components, and properties of an identity matrix
21. Reviewed definition, concepts, notation, terminology, components, and properties of the adjugate of a square matrix, including procedures to form the adjugate of a square matrix
22. Reviewed definition, concepts, notation, terminology, components, and properties of the matrix inverse formula
23. Reviewed definition, concepts, notation, terminology, components, and properties of a singular matrix
24. Reviewed definition, concepts, notation, terminology, components, properties, rules, and procedures for calculating the inverse of a 2×2 matrix, 3×3 matrix, 4×4 matrix and higher
25. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for performing the tasks and calculations for calculating the inverse of a 2×2 matrix, 3×3 matrix, 4×4 matrix and higher
26. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of most used methods for solving systems of equations using matrices and the Gaussian elimination method
27. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of most used methods for solving systems of equations using matrices and Cramer’s Rule
28. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of most used methods for solving systems of equations using matrices and the Gauss-Jordan elimination method
29. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of most used methods for solving systems of equations using matrices and the matrix inverse method
30. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for performing the tasks and calculations for most used methods for solving systems of equations using matrices (Gaussian elimination method, Cramer’s Rule, Gauss-Jordan elimination method, and matrix inverse method)
31. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of matrix transformations in general
32. Reviewed definition, concepts, notation, terminology, components, properties, and applicability, and procedures of matrix transformation by rotation
33. Reviewed definition, concepts, notation, terminology, components, properties, and applicability, and procedures of matrix transformation by scaling
34. Reviewed definition, concepts, notation, terminology, components, properties, and applicability, and procedures of matrix transformation by reflection
35. Reviewed definition, concepts, notation, terminology, components, properties, and applicability, and procedures of matrix transformation by shearing
36. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for performing the tasks and calculations for matrix transformations for rotation, scaling, reflection, and shearing
37. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of matrix transformations for normalization (aka feature scaling)
38. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of matrix transformations for standardization
39. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of matrix transformations for dimensionality reduction
40. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of matrix transformations for feature engineering
41. Reviewed definition, concepts, notation, terminology, components, properties, applicability, and analysis of the properties of an inverse of a matrix
42. Reviewed definition, concepts, notation, terminology, components, properties, applicability, and analysis of the properties of the transpose of a matrix
43. Reviewed definition, concepts, notation, terminology, components, properties, applicability, and analysis of the properties of matrix types
44. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for analyzing the properties of an inverse of a matrix
45. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for analyzing the properties of the transpose of a matrix
46. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for analyzing matrix types
47. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of using a connectivity matrix for network analysis
48. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of using an adjacency matrix for network analysis
49. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of using a degree matrix for network analysis
50. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of using a Laplacian matrix for network analysis
51. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of using an incidence matrix for network analysis
52. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for matrix network analysis
53. Reviewed definition, concepts, notation, terminology, components, properties, and applicability of interpreting matrix operations in data contexts
54. Reviewed similarities and differences in the applicability and analysis of types of linear models (simple linear regression, multiple linear regression, multivariate linear regression, general linear model (GLM), hierarchical linear models (HLD), and structural equation models (SEM))
55. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for interpreting matrix operations in data contexts
56. Reviewed how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for building types of linear models (simple linear regression, multiple linear regression, multivariate linear regression, general linear model (GLM), hierarchical linear models (HLD), and structural equation models (SEM))

Part 1 of 10

Goal 1 Statement: Review definition, concepts, notation, terminology, components, and properties of matrices

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review definition, concepts, notation, terminology, components, properties, rules, and procedures for matrix addition

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Goal 3 Statement: Review definition, concepts, notation, terminology, components, properties, rules, and procedures for matrix subtraction

Goal 3 Plan: Read source materials

Goal 3 Work Product: None

Goal 3 Result: Completed

Goal 4 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for performing the tasks and calculations for matrix addition

Goal 4 Plan: Read source materials

Goal 4 Work Product: None

Goal 4 Result: Completed

Goal 5 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for performing the tasks and calculations for matrix subtraction

Goal 5 Plan: Read source materials

Goal 5 Work Product: None

Goal 5 Result: Completed

Part 2 of 10

Goal 1 Statement: Review definition, concepts, notation, terminology, components, and properties of a scalar and scalar matrix

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review definition, concepts, notation, terminology, components, and properties of a vector

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Goal 3 Statement: Review definition, concepts, notation, terminology, components, and properties of a covariance matrix

Goal 3 Plan: Read source materials

Goal 3 Work Product: None

Goal 3 Result: Completed

Goal 4 Statement: Review definition, concepts, notation, terminology, components, and properties of a correlation matrix

Goal 4 Plan: Read source materials

Goal 4 Work Product: None

Goal 4 Result: Completed

Goal 5 Statement: Review similarities and differences between covariance and correlation matrix

Goal 5 Plan: Read source materials

Goal 5 Work Product: None

Goal 5 Result: Completed

Goal 6 Statement: Review definition, concepts, notation, terminology, components, and properties of an eigenvalue and eigenvector

Goal 6 Plan: Read source materials

Goal 6 Work Product: None

Goal 6 Result: Completed

Goal 7 Statement: Review definition, concepts, notation, terminology, components, and properties of the determinant of a matrix

Goal 7 Plan: Read source materials

Goal 7 Work Product: None

Goal 7 Result: Completed

Goal 8 Statement: Review definition, concepts, notation, terminology, components, and properties of the dot product (aka scalar product)

Goal 8 Plan: Read source materials

Goal 8 Work Product: None

Goal 8 Result: Completed

Goal 9 Statement: Review definition, concepts, notation, terminology, components, properties, rules, and procedures for matrix multiplication, including the dot product (aka scalar product)

Goal 9 Plan: Read source materials

Goal 9 Work Product: None

Goal 9 Result: Completed

Goal 10 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for performing the tasks and calculations for matrix multiplication, including the dot product (aka scalar product)

Goal 10 Plan: Read source materials

Goal 10 Work Product: None

Goal 10 Result: Completed

Part 3 of 10

Goal 1 Statement: Review definition, concepts, notation, terminology, components, and properties of the determinant formula

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review definition, concepts, notation, terminology, components, and properties of cofactor expansion (aka Laplace expansion)

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Goal 3 Statement: Review definition, concepts, notation, terminology, components, properties, rules, and procedures for calculating the determinant of a 2×2 matrix, 3×3 matrix, 4×4 matrix and higher

Goal 3 Plan: Read source materials

Goal 3 Work Product: None

Goal 3 Result: Completed

Goal 4 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for performing the tasks and calculations for calculating determinant of a 2×2 matrix, 3×3 matrix, 4×4 matrix and higher

Goal 4 Plan: Read source materials

Goal 4 Work Product: None

Goal 4 Result: Completed

Part 4 of 10

Goal 1 Statement: Review definition, concepts, notation, terminology, components, and properties of an identity matrix

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review definition, concepts, notation, terminology, components, and properties of the adjugate of a square matrix, including procedures to form the adjugate of a square matrix

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Goal 3 Statement: Review definition, concepts, notation, terminology, components, and properties of the matrix inverse formula

Goal 3 Plan: Read source materials

Goal 3 Work Product: None

Goal 3 Result: Completed

Goal 4 Statement: Review definition, concepts, notation, terminology, components, and properties of a singular matrix

Goal 4 Plan: Read source materials

Goal 4 Work Product: None

Goal 4 Result: Completed

Goal 5 Statement: Review definition, concepts, notation, terminology, components, properties, rules, and procedures for calculating the inverse of a 2×2 matrix, 3×3 matrix, 4×4 matrix and higher

Goal 5 Plan: Read source materials

Goal 5 Work Product: None

Goal 5 Result: Completed

Goal 6 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for performing the tasks and calculations for calculating the inverse of a 2×2 matrix, 3×3 matrix, 4×4 matrix and higher

Goal 6 Plan: Read source materials

Goal 6 Work Product: None

Goal 6 Result: Completed

Part 5 of 10

Goal 1 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of most used methods for solving systems of equations using matrices and the Gaussian elimination method

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of most used methods for solving systems of equations using matrices and Cramer’s Rule

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Goal 3 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of most used methods for solving systems of equations using matrices and the Gauss-Jordan elimination method

Goal 3 Plan: Read source materials

Goal 3 Work Product: None

Goal 3 Result: Completed

Goal 4 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of most used methods for solving systems of equations using matrices and the matrix inverse method

Goal 4 Plan: Read source materials

Goal 4 Work Product: None

Goal 4 Result: Completed

Goal 5 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for performing the tasks and calculations for most used methods for solving systems of equations using matrices (Gaussian elimination method, Cramer’s Rule, Gauss-Jordan elimination method, and matrix inverse method)

Goal 5 Plan: Read source materials

Goal 5 Work Product: None

Goal 5 Result: Completed

Part 6 of 10

Goal 1 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of matrix transformations in general

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability, and procedures of matrix transformation by rotation

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Goal 3 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability, and procedures of matrix transformation by scaling

Goal 3 Plan: Read source materials

Goal 3 Work Product: None

Goal 3 Result: Completed

Goal 4 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability, and procedures of matrix transformation by reflection

Goal 4 Plan: Read source materials

Goal 4 Work Product: None

Goal 4 Result: Completed

Goal 5 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability, and procedures of matrix transformation by shearing

Goal 5 Plan: Read source materials

Goal 5 Work Product: None

Goal 5 Result: Completed

Goal 6 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for performing the tasks and calculations for matrix transformations for rotation, scaling, reflection, and shearing

Goal 6 Plan: Read source materials

Goal 6 Work Product: None

Goal 6 Result: Completed

Part 7 of 10

Goal 1 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of matrix transformations for normalization (aka feature scaling)

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of matrix transformations for standardization

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Goal 3 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of matrix transformations for dimensionality reduction

Goal 3 Plan: Read source materials

Goal 3 Work Product: None

Goal 3 Result: Completed

Goal 4 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of matrix transformations for feature engineering

Goal 4 Plan: Read source materials

Goal 4 Work Product: None

Goal 4 Result: Completed

Goal 5 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for performing the tasks and calculations for matrix transformations for normalization, standardization, dimensionality reduction, and feature engineering

Goal 5 Plan: Read source materials

Goal 5 Work Product: None

Goal 5 Result: Completed

Part 8 of 10

Goal 1 Statement: Review definition, concepts, notation, terminology, components, properties, applicability, and analysis of the properties of an inverse of a matrix

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review definition, concepts, notation, terminology, components, properties, applicability, and analysis of the properties of the transpose of a matrix

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Goal 3 Statement: Review definition, concepts, notation, terminology, components, properties, applicability, and analysis of the properties of matrix types

Goal 3 Plan: Read source materials

Goal 3 Work Product: None

Goal 3 Result: Completed

Goal 4 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for analyzing the properties of an inverse of a matrix

Goal 4 Plan: Read source materials

Goal 4 Work Product: None

Goal 4 Result: Completed

Goal 5 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for analyzing the properties of the transpose of a matrix

Goal 5 Plan: Read source materials

Goal 5 Work Product: None

Goal 5 Result: Completed

Goal 6 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for analyzing matrix types

Goal 6 Plan: Read source materials

Goal 6 Work Product: None

Goal 6 Result: Completed

Part 9 of 10

Goal 1 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of using a connectivity matrix for network analysis

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of using an adjacency matrix for network analysis

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Goal 3 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of using a degree matrix for network analysis

Goal 3 Plan: Read source materials

Goal 3 Work Product: None

Goal 3 Result: Completed

Goal 4 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of using a Laplacian matrix for network analysis

Goal 4 Plan: Read source materials

Goal 4 Work Product: None

Goal 4 Result: Completed

Goal 5 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of using an incidence matrix for network analysis

Goal 5 Plan: Read source materials

Goal 5 Work Product: None

Goal 5 Result: Completed

Goal 6 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for matrix network analysis

Goal 6 Plan: Read source materials

Goal 6 Work Product: None

Goal 6 Result: Completed

Part 10 of 10

Goal 1 Statement: Review definition, concepts, notation, terminology, components, properties, and applicability of interpreting matrix operations in data contexts

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review similarities and differences in the applicability and analysis of types of linear models (simple linear regression, multiple linear regression, multivariate linear regression, general linear model (GLM), hierarchical linear models (HLD), and structural equation models (SEM))

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Goal 3 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for interpreting matrix operations in data contexts

Goal 3 Plan: Read source materials

Goal 3 Work Product: None

Goal 3 Result: Completed

Goal 4 Statement: Review how Python, Julia, R, SQL, and other computer programming languages and applications are utilized for building types of linear models (simple linear regression, multiple linear regression, multivariate linear regression, general linear model (GLM), hierarchical linear models (HLD), and structural equation models (SEM))

Goal 4 Plan: Read source materials

Goal 4 Work Product: None

Goal 4 Result: Completed