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Further Matrix Algebra

Def. Def. 2 x 2. e.g. 3 x 3. e.g. Further Matrix Algebra. e.g. In general. In general. Transpose of a matrix. Ex. Transpose of a matrix. Ex. Transpose of a matrix. Ex. Res. Further Matrix Algebra. Page 142 Exercise 6A. Def. Ex. Further Matrix Algebra. FP1. Ex.

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Further Matrix Algebra

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  1. Def. Def. 2 x 2 e.g. 3 x 3 e.g. Further Matrix Algebra e.g. In general In general

  2. Transpose of a matrix Ex

  3. Transpose of a matrix Ex

  4. Transpose of a matrix Ex

  5. Res. Further Matrix Algebra Page 142 Exercise 6A

  6. Def. Ex Further Matrix Algebra FP1

  7. Ex Further Matrix Algebra FP1

  8. Transpose of a matrix Ex

  9. Transpose of a matrix Ex Page 146 Exercise 6B

  10. FP1 FP1 Inverse Matrices FP1

  11. Ex Inverse Matrices Def. Minor The minor of an element is the determinant of the elements which remain when the row and column containing the element are crossed out.

  12. Def. Matrix of cofactors Inverse Matrices Def. Matrix of minors The matrix of minors M of a matrix A is found by replacing each element of A with the minor of that element.

  13. Ex Inverse Matrices Def.

  14. Ex Inverse Matrices

  15. Inverse Matrices Res. Proof

  16. Inverse Matrices Ex Page 151 Exercise 6C

  17. Range Domain Example Vector Functions Idea The domain or range of a function can have more than one dimension! 1 1 1 2 3 1

  18. Range Domain Example Vector Functions Idea The domain or range of a function can have more than one dimension! 2 2 3 3

  19. ? L1 L2 Linear Functions Linear Function Def. L1 L2

  20. Ex Linear Transformations Idea

  21. Linear Transformations Ex

  22. Linear Transformations Ex

  23. Linear Transformations Ex

  24. Linear Transformations Ex Page 159 Exercise 6D

  25. Linear Transformations Ex

  26. Linear Transformations Ex

  27. Ex Linear Transformations Idea Don’t find the inverse matrix unless you have to. Page 164 Exercise 6E

  28. Eigenvalues and Eigenvectors Idea There will be some vectors for which the effect of a linear transformation is just like being multiplied by a scalar!

  29. Idea Finding eigenvalues Eigenvalues and Eigenvectors Eigenvectors and Eigenvalues Def.

  30. Idea Normalised vector Def. Eigenvalues and Eigenvectors Characterstic Equation Def.

  31. Eigenvalues and Eigenvectors Ex

  32. Eigenvalues and Eigenvectors Ex

  33. Eigenvalues and Eigenvectors Ex

  34. Eigenvalues and Eigenvectors Ex

  35. Eigenvalues and Eigenvectors Ex Page 164 Exercise 6F

  36. Res. Diagonal Form Def. Orthogonal

  37. Diagonalisation Res. Diagonal Form Def. Diagonal Matrix

  38. ? Diagonal Form Res.

  39. Diagonal Form Ex

  40. Diagonal Form Ex

  41. Diagonal Form Ex

  42. Diagonal Form Ex Page 186 Exercise 6G

  43. Labels M1 Reference to previous module 1 ? Quick Question Def. Definition Idea Key Idea Ex Example Ex Exercise

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