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Linear Algebra: A Pure Mathematical Approach
Hardcover
Publisher Price: $99.00
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ISBN10: 3764369051
ISBN13: 9783764369057
Publisher: Springer Nature
Published: Oct 3 2002
Pages: 268
Weight: 1.22
Height: 0.63 Width: 6.14 Depth: 9.21
Language: English
ISBN13: 9783764369057
Publisher: Springer Nature
Published: Oct 3 2002
Pages: 268
Weight: 1.22
Height: 0.63 Width: 6.14 Depth: 9.21
Language: English
1 - Algebraic Preamble.- Groups, Rings and Fields.- Permutation Groups.- Problems 1.- 2 - Vector Spaces and Linear Maps.- Vector Spaces and Algebras.- Bases and Dimension.- Linear Maps.- Direct Sums.- Addendum - Modules.- Problems 2.- 3 - Matrices, Determinants and Linear Equations.- Matrices.- Determinants.- Systems of Linear Equations.- Problems 3.- 4 - Cayley-Hamilton Theorem and Jordan Form.- Polynomials.- Cayley-Hamilton and Spectral Theorems.- Jordan Form.- Problems 4.- 5 - Interlude on Finite Fields.- Finite Fields.- Applications - Linear Codes and Finite Matrix Groups.- Problems 5.- 6 - Hermitian and Inner Product Spaces.- Hermitian and Inner Products, and Norms.- Unitary and Self-adjoint Maps.- Orthogonal and Symmetric Maps.- Problems 6.- 7 - Selected Topics.- The Geometry of Real Quadratic Forms.- Normed Algebras, Quaternions and Cayley Numbers.- to the Representation of Finite Groups.- Problems 7.- Appendix A - Set Theory.- Sets and Maps.- Problems A.- Appendix B - Answers and Solutions to the Problems.- Notation Index.- Definition Index.- Theorem Index.
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