Math 2.0

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Linear Algebra JXS2JMS2W2

URIm2://res/JXS2JMS2W2
Kindcourse
CreatorsK.C. Sivakumar (instructor)
Date2015-02-05
Scopein
Idscourse 03v0r5n49:111106051

Expressions

e1: edition

Languageen
Date2015-02-05
Contents
  • part 1: SYSTEMS OF LINEAR EQUATIONS
  • session 1: 1. Introduction to the Course Contents.
  • session 2: 2. Linear Equations
  • session 3: 3a. Equivalent Systems of Linear Equations I: Inverses of Elementary Row-operations, Row-equivalent matrices
  • session 4: 3b. Equivalent Systems of Linear Equations II: Homogeneous Equations, Examples
  • session 5: 4. Row-reduced Echelon Matrices
  • session 6: 5. Row-reduced Echelon Matrices and Non-homogeneous Equations
  • session 7: 6. Elementary Matrices, Homogeneous Equations and Non-homogeneous Equations
  • session 8: 7. Invertible matrices, Homogeneous Equations Non-homogeneous Equations
  • part 2: VECTOR SPACES
  • session 9: 8. Vector spaces
  • session 10: 9. Elementary Properties in Vector Spaces. Subspaces
  • session 11: 10. Subspaces (continued), Spanning Sets, Linear Independence, Dependence
  • part 3: BASIS AND DIMENSION
  • session 12: 11. Basis for a vector space
  • session 13: 12. Dimension of a vector space
  • session 14: 13. Dimensions of Sums of Subspaces
  • part 4: LINEAR TRANSFORMATIONS
  • session 15: 14. Linear Transformations
  • session 16: 15. The Null Space and the Range Space of a Linear Transformation
  • session 17: 16. The Rank-Nullity-Dimension Theorem. Isomorphisms Between Vector Spaces
  • session 18: 17. Isomorphic Vector Spaces, Equality of the Row-rank and the Column-rank I
  • session 19: 18. Equality of the Row-rank and the Column-rank II
  • part 5: MATRIX OF A LINEAR TRANSFORMATION
  • session 20: 19. The Matrix of a Linear Transformation
  • session 21: 20. Matrix for the Composition and the Inverse. Similarity Transformation
  • part 6: THE DUAL SPACE
  • session 22: 21. Linear Functionals. The Dual Space. Dual Basis I
  • session 23: 22. Dual Basis II. Subspace Annihilators I
  • session 24: 23. Subspace Annihilators II
  • session 25: 24. The Double Dual. The Double Annihilator
  • session 26: 25. The Transpose of a Linear Transformation. Matrices of a Linear Transformation and its Transpose
  • part 7: EIGENVALUES AND EIGENVECTORS
  • session 27: 26. Eigenvalues and Eigenvectors of Linear Operators
  • session 28: 27. Diagonalization of Linear Operators. A Characterization
  • session 29: 28. The Minimal Polynomial
  • session 30: 29. The Cayley-Hamilton Theorem
  • part 8: INVARIANT SUBSPACES AND TRIANGULABILITY
  • session 31: 30. Invariant Subspaces
  • session 32: 31. Triangulability, Diagonalization in Terms of the Minimal Polynomial
  • session 33: 32. Independent Subspaces and Projection Operators
  • part 9: DIRECT SUM DECOMPOSITIONS
  • session 34: 33. Direct Sum Decompositions and Projection Operators I
  • session 35: 34. Direct Sum Decomposition and Projection Operators II
  • part 10: PRIMARY AND CYCLIC DECOMPOSITION THEOREMS
  • session 36: 35. The Primary Decomposition Theorem and Jordan Decomposition
  • session 37: 36. Cyclic Subspaces and Annihilators
  • session 38: 37. The Cyclic Decomposition Theorem I
  • session 39: 38. The Cyclic Decomposition Theorem II. The Rational Form
  • part 11: INNER PRODUCT SPACES
  • session 40: 39. Inner Product Spaces
  • session 41: 40. Norms on Vector spaces. The Gram-Schmidt Procedure I
  • session 42: 41. The Gram-Schmidt Procedure II. The QR Decomposition.
  • session 43: 42. Bessel's Inequality, Parseval's Indentity, Best Approximation
  • part 12: BEST APPROXIMATION
  • session 44: 43. Best Approximation: Least Squares Solutions
  • session 45: 44. Orthogonal Complementary Subspaces, Orthogonal Projections
  • session 46: 45. Projection Theorem. Linear Functionals
  • part 13: ADJOINT OF A LINEAR OPERATOR
  • session 47: 46. The Adjoint Operator
  • session 48: 47. Properties of the Adjoint Operation. Inner Product Space Isomorphism
  • part 14: SELF-ADJOINT, NORMAL AND UNITARY OPERATORS
  • session 49: 48. Unitary Operators
  • session 50: 49. Unitary operators II. Self-Adjoint Operators I.
  • session 51: 50. Self-Adjoint Operators II - Spectral Theorem
  • session 52: 51. Normal Operators - Spectral Theorem

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