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David J. Krus presents Matrix Algebra for Social Sciences. Introduction to Matrix Algebra. Dimensions of a Matrix. Number of Rows: 2 Number of Columns:3 A 2 x 3 Matrix. Elements of a Matrix. Principal Diagonal Elements . Off-Diagonal Elements . Nomenclature of Matrices. Rectangular

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David J. Krus presents Matrix Algebra for Social Sciences


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    1. David J. KruspresentsMatrix Algebrafor Social Sciences

    2. Introduction toMatrix Algebra

    3. Dimensions of a Matrix • Number of Rows: 2 • Number of Columns:3 • A 2 x 3 Matrix

    4. Elements of a Matrix

    5. Principal Diagonal Elements

    6. Off-Diagonal Elements

    7. Nomenclature of Matrices • Rectangular • Square • Symmetric • Skew Symmetric

    8. Transpose

    9. Triangulation

    10. Matrix Algebra Operations on Matrix Elements

    11. Addition of Matrix Elements • All matrices must have the the same dimensions. • The plus sign is enclosed in parentheses. 2 x 2 2 x 2 2 x 2

    12. Addition of Matrix Elements

    13. Subtraction of Matrix Elements • All matrices must have the the same dimensions. • The subtraction sign is enclosed in parentheses. 2 x 2 2 x 2 2 x 2

    14. Subtraction of Matrix Elements

    15. Multiplication of Matrix Elements • All matrices must have the the same dimensions. • The multiplication sign is enclosed in parentheses. 2 x 2 2 x 2 2 x 2

    16. Multiplication of Matrix Elements

    17. Division of Matrix Elements • All matrices must have the the same dimensions or the divisor must be a scalar number. • The division sign is enclosed in parentheses. 2 x 2 2 x 2 2 x 2

    18. Division of Matrix Elements

    19. Powers of Matrix Elements • The square sign is enclosed in parentheses.

    20. Powers of Matrix Elements • The square sign is enclosed in parentheses

    21. Matrix Algebra Operations on Matrices

    22. Addition of Matrices 3 x 1 1 x 3 3 x 3

    23. Major Addition of Matrices 1 + 1 = 2 1 + 2 = 3 1 + 3 = 4

    24. Major Addition of Matrices 2 + 1 = 3 2 + 2 = 4 2 + 3 = 5

    25. Major Addition of Matrices 3 + 1 = 4 3 + 2 = 5 3 + 3 = 6

    26. Minor Addition of Matrices (1+1) + (2+2) + (3+3) = 12

    27. Subtraction of Matrices 1 x 3 3 x 1 1 x 1

    28. Minor Subtraction of Matrices (1-1) + (2-2) + (3-3) =0

    29. Major Subtraction of Matrices 1 - 1 = 0 1 - 2 = -1 1 - 3 = -2

    30. Major Subtraction of Matrices 2 - 1 = 1 2 - 2 = 0 2 - 3 = -1

    31. Major Subtraction of Matrices 3 - 1 = 2 3 - 2 = 1 3 - 3 = 0

    32. Multiplication of Matrices 3 x 2 2 x 3 3 x 3

    33. Multiplication of Matrices (1*7) + (2*10) =27 (1*8) + (2*11) =30 (1*9) + (2*12) =33

    34. Multiplication of Matrices (3*7) + (4*10) = 61 (3*8) + (4*11) = 68 (3*9) + (4*12) = 75

    35. Multiplication of Matrices (5*7) + (6*10) = 95 (5*8) + (6*11) = 106 (5*9) + (6*12) = 117

    36. Matrix Inversion

    37. Matrix Inversion

    38. Matrix Inversion

    39. Powers of Matrices

    40. Powers of Matrices (1*1) + (2*3) = 7 (1*2) + (2*4) = 10 (3*1) + (4*3) = 15 (3*2) + (4*4) = 22

    41. Elements Of Statistics

    42. Algebraic Mean In Summation Notation

    43. Summation Notation

    44. Algebraic Mean In Matrix Algebra Notation

    45. Matrix Algebra Notation

    46. Matrix Multiplication

    47. Mean

    48. True Variance In Summation Notation

    49. Summation Notation

    50. True Variance In Matrix Algebra Notation