Page 5 - DMTH502_LINEAR_ALGEBRA

CONTENT

Unit 1: Vector Space over Fields 1
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Unit 2: Vector Subspaces 61
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Unit 3: Bases and Dimensions of Vector Spaces 69
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Unit 4: Co-ordinates 75
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Unit 5: Summary of Row-Equivalence 85
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Unit 6: Computation Concerning Subspaces 97
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Unit 7: Algebra of Linear Transformation 103
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Unit 8: Isomorphism 118
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Unit 9: Representation of Transformations by Matrices 122
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Unit 10: Linear Functionals 133
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Unit 11: The Double Dual 144
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Unit 12: Introduction and Characteristic Values of Elementary Canonical Forms 155
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Unit 13: Annihilating Polynomials 167
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Unit 14: Invariant Subspaces 177
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Unit 15: Simultaneous Triangulation and Simultaneous Diagonalization 184
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Unit 16: Direct Sum Decompositions of Elementary Canonical Forms 188
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Unit 17: Invariant Direct Sums 193
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Unit 18: The Primary Decomposition Theorem 199
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