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“A Quick Introduction to Group Representations”, by Amit Kulshrestha

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“Basic Properties of Groups and Multiplication Tables”, by Krishna Hanumanthu

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“Definition of a Group and Examples”;, by Krishna Hanumanthu

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“More Examples of Groups”;, by Krishna Hanumanthu

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“Motivational Examples of Groups”;, by Krishna Hanumanthu

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1. Introduction to the Course Contents., by K.C. Sivakumar

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10 Points on an Equilateral Triangle, by Sudarshan Iyengar

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10. Subspaces (Continued) , Spanning Sets, Linear Independence, Dependence, by K.C. Sivakumar

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11. Basis for a Vector Space, by K.C. Sivakumar

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12. Dimension of a Vector Space, by K.C. Sivakumar

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13. Dimensions of Sums of Subspaces, by K.C. Sivakumar

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14. Linear Transformations, by K.C. Sivakumar

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15. the Null Space and the Range Space of a Linear Transformation, by K.C. Sivakumar

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16. the Rank-Nullity-Dimension Theorem. Isomorphisms between Vector Spaces, by K.C. Sivakumar

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17. Isomorphic Vector Spaces, Equality of the Row-Rank and the Column-Rank I, by K.C. Sivakumar

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18. Equality of the Row-Rank and the Column-Rank II, by K.C. Sivakumar

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19. the Matrix of a Linear Transformation, by K.C. Sivakumar

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2 by 2 Systems and Phase Plane Analysis Continued, by Raju K. George

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2 by 2 Systems and Phase Plane Analysis, by Raju K. George

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2-Connected Graphs 1, by Soumen Maity

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2-Connected Graphs, by Soumen Maity

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2. Linear Equations, by K.C. Sivakumar

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20. Matrix for the Composition and the Inverse. Similarity Transformation, by K.C. Sivakumar

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21. Linear Functionals. the Dual Space. Dual Basis I, by K.C. Sivakumar

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22. Dual Basis II. Subspace Annihilators I, by K.C. Sivakumar

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23. Subspace Annihilators II, by K.C. Sivakumar

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24. the Double Dual. the Double Annihilator, by K.C. Sivakumar

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25. the Transpose of a Linear Transformation. Matrices of a Linear Transformation and its Transpose, by K.C. Sivakumar

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26. Eigenvalues and Eigenvectors of Linear Operators, by K.C. Sivakumar

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27. Diagonalization of Linear Operators. a Characterization, by K.C. Sivakumar

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28. the Minimal Polynomial, by K.C. Sivakumar

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29. the Cayley-Hamilton Theorem, by K.C. Sivakumar

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2Nd Uniqueness Theorem, Artinian Rings, by A.V.Jayanthan

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3 Utilities Problem-Revisited, by Sudarshan Iyengar

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30. Invariant Subspaces, by K.C. Sivakumar

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31. Triangulability, Diagonalization in Terms of the Minimal Polynomial, by K.C. Sivakumar

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32. Independent Subspaces and Projection Operators, by K.C. Sivakumar

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33. Direct Sum Decompositions and Projection Operators I, by K.C. Sivakumar

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34. Direct Sum Decomposition and Projection Operators II, by K.C. Sivakumar

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35. the Primary Decomposition Theorem and Jordan Decomposition, by K.C. Sivakumar

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36. Cyclic Subspaces and Annihilators, by K.C. Sivakumar

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37. the Cyclic Decomposition Theorem I, by K.C. Sivakumar

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38. the Cyclic Decomposition Theorem II. the Rational Form, by K.C. Sivakumar

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39. Inner Product Spaces, by K.C. Sivakumar

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3a. Equivalent Systems of Linear Equations I: Inverses of Elementary Row-Operations, Row-Equivalent Matrices, by K.C. Sivakumar

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3b. Equivalent Systems of Linear Equations II: Homogeneous Equations, Examples, by K.C. Sivakumar

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4. Row-Reduced Echelon Matrices, by K.C. Sivakumar

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40. Norms on Vector spaces. the Gram-Schmidt Procedure I, by K.C. Sivakumar

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41. the Gram-Schmidt Procedure II. the QR Decomposition., by K.C. Sivakumar

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42. Bessel’s Inequality, Parseval’s Indentity, best Approximation, by K.C. Sivakumar

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