Linear Algebra

Linear Algebra

nptelhrd via YouTube Direct link

Mod-01 Lec-01 Introduction to the Course Contents.

1 of 52

1 of 52

Mod-01 Lec-01 Introduction to the Course Contents.

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Linear Algebra

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  1. 1 Mod-01 Lec-01 Introduction to the Course Contents.
  2. 2 Mod-01 Lec-02 Linear Equations
  3. 3 Mod-01 Lec-03a Equivalent Systems of Linear Equations I: Inverses of Elementary Row-operations
  4. 4 Mod-01 Lec-03b Equivalent Systems of Linear Equations II: Homogeneous Equations, Examples
  5. 5 Mod-01 Lec-04 Row-reduced Echelon Matrices
  6. 6 Mod-01 Lec-05 Row-reduced Echelon Matrices and Non-homogeneous Equations
  7. 7 Mod-01 Lec-06 Elementary Matrices, Homogeneous Equations and Non-homogeneous Equations
  8. 8 Mod-01 Lec-07 Invertible matrices, Homogeneous Equations Non-homogeneous Equations
  9. 9 Mod-02 Lec-08 Vector spaces
  10. 10 Mod-02 Lec-09 Elementary Properties in Vector Spaces. Subspaces
  11. 11 Mod-02 Lec-10 Subspaces (continued), Spanning Sets, Linear Independence, Dependence
  12. 12 Mod-03 Lec-11 Basis for a vector space
  13. 13 Mod-03 Lec-12 Dimension of a vector space
  14. 14 Mod-03 Lec-13 Dimensions of Sums of Subspaces
  15. 15 Mod-04 Lec-14 Linear Transformations
  16. 16 Mod-04 Lec-15 The Null Space and the Range Space of a Linear Transformation
  17. 17 Mod-04 Lec-16 The Rank-Nullity-Dimension Theorem. Isomorphisms Between Vector Spaces
  18. 18 Mod-04 Lec-17 Isomorphic Vector Spaces, Equality of the Row-rank and the Column-rank I
  19. 19 Mod-04 Lec-18 Equality of the Row-rank and the Column-rank II
  20. 20 Mod-05 Lec19 The Matrix of a Linear Transformation
  21. 21 Mod-05 Lec-20 Matrix for the Composition and the Inverse. Similarity Transformation
  22. 22 Mod-06 Lec-21 Linear Functionals. The Dual Space. Dual Basis I
  23. 23 Mod-06 Lec-22 Dual Basis II. Subspace Annihilators I
  24. 24 Mod-06 Lec-23 Subspace Annihilators II
  25. 25 Mod-06 Lec-24 The Double Dual. The Double Annihilator
  26. 26 Mod-06 Lec-25 The Transpose of a Linear Transformation. Matrices of a Linear
  27. 27 Mod-07 Lec-26 Eigenvalues and Eigenvectors of Linear Operators
  28. 28 Mod-07 Lec-27 Diagonalization of Linear Operators. A Characterization
  29. 29 Mod-07 Lec-28 The Minimal Polynomial
  30. 30 Mod-07 Lec-29 The Cayley-Hamilton Theorem
  31. 31 Mod-08 Lec-30 Invariant Subspaces
  32. 32 Mod-08 Lec-31 Triangulability, Diagonalization in Terms of the Minimal Polynomial
  33. 33 Mod-08 Lec-32 Independent Subspaces and Projection Operators
  34. 34 Mod-09 Lec-33 Direct Sum Decompositions and Projection Operators I
  35. 35 Mod-09 Lec-34 Direct Sum Decomposition and Projection Operators II
  36. 36 Mod-10 Lec-35 The Primary Decomposition Theorem and Jordan Decomposition
  37. 37 Mod-10 Lec-36 Cyclic Subspaces and Annihilators
  38. 38 Mod-10 Lec-37 The Cyclic Decomposition Theorem I
  39. 39 Mod-10 Lec-38 The Cyclic Decomposition Theorem II. The Rational Form
  40. 40 Mod-11 Lec-39 Inner Product Spaces
  41. 41 Mod-11 Lec-40 Norms on Vector spaces. The Gram-Schmidt Procedure I
  42. 42 Mod-11 Lec-41 The Gram-Schmidt Procedure II. The QR Decomposition.
  43. 43 Mod-11 Lec-42 Bessel's Inequality, Parseval's Indentity, Best Approximation
  44. 44 Mod-12 Lec-43 Best Approximation: Least Squares Solutions
  45. 45 Mod-12 Lec-44 Orthogonal Complementary Subspaces, Orthogonal Projections
  46. 46 Mod-12 Lec-45 Projection Theorem. Linear Functionals
  47. 47 Mod-13 Lec-46 The Adjoint Operator
  48. 48 Mod-13 Lec-47 Properties of the Adjoint Operation. Inner Product Space Isomorphism
  49. 49 Mod-14 Lec-48 Unitary Operators
  50. 50 Mod-14 Lec-49 Unitary operators II. Self-Adjoint Operators I.
  51. 51 Mod-14 Lec-50 Self-Adjoint Operators II - Spectral Theorem
  52. 52 Mod-14 Lec-51 Normal Operators - Spectral Theorem

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