'16. The Rank-Nullity-Dimension Theorem. Isomorphisms Between Vector Spaces' Video Lecture

Course Video Lectures 1. Introduction to the Course Contents. 2. Linear Equations 3a. Equivalent Systems of Linear Equations I:.. 3b. Equivalent Systems of Linear Equations II.. 4. Row-reduced Echelon Matrices 5. Row-reduced Echelon Matrices and Non-homog.. 6. Elementary Matrices, Homogeneous Equations.. 7. Invertible matrices, Homogeneous Equations.. 8. Vector spaces 9. Elementary Properties in Vector Spaces. Su.. 10. Subspaces (continued), Spanning Sets, Lin.. 11. Basis for a vector space 12. Dimension of a vector space 13. Dimensions of Sums of Subspaces 14. Linear Transformations 15. The Null Space and the Range Space of a L.. 16. The Rank-Nullity-Dimension Theorem. Isomo.. 17. Isomorphic Vector Spaces, Equality of the.. 18. Equality of the Row-rank and the Column-r.. 19. The Matrix of a Linear Transformation 20. Matrix for the Composition and the Invers.. 21. Linear Functionals. The Dual Space. Dual .. 22. Dual Basis II. Subspace Annihilators I 23. Subspace Annihilators II 24. The Double Dual. The Double Annihilator 25. The Transpose of a Linear Transformation... 26. Eigenvalues and Eigenvectors of Linear Op.. 27. Diagonalization of Linear Operators. A Ch.. 28. The Minimal Polynomial 29. The Cayley-Hamilton Theorem 30. Invariant Subspaces 31. Triangulability, Diagonalization in Terms.. 32. Independent Subspaces and Projection Oper.. 33. Direct Sum Decompositions and Projection .. 34. Direct Sum Decomposition and Projection O.. 35. The Primary Decomposition Theorem and Jor.. 36. Cyclic Subspaces and Annihilators 37. The Cyclic Decomposition Theorem I 38. The Cyclic Decomposition Theorem II. The .. 39. Inner Product Spaces 40. Norms on Vector spaces. The Gram-Schmidt .. 41. The Gram-Schmidt Procedure II. The QR Dec.. 42. Bessel's Inequality, Parseval's Indentity.. 43. Best Approximation: Least Squares Solutio.. 44. Orthogonal Complementary Subspaces, Ortho.. 45. Projection Theorem. Linear Functionals 46. The Adjoint Operator 47. Properties of the Adjoint Operation. Inne.. 48. Unitary Operators 49. Unitary operators II. Self-Adjoint Operat.. 50. Self-Adjoint Operators II - Spectral Theo.. 51. Normal Operators - Spectral Theorem