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Linear Algebra: A Pure Mathematical Approach by H. E. Rose

Linear Algebra: A Pure Mathematical Approach

by H. E. Rose
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Book cover type: Hardcover
  • ISBN13: 9783764369057
  • Binding: Hardcover
  • Subject: N/A
  • Publisher: Birkhauser
  • Publisher Imprint: Birkhauser
  • Publication Date:
  • Pages: 250
  • Original Price: EUR 79.95
  • Language: English
  • Edition: N/A
  • Item Weight: 554 grams
  • BISAC Subject(s): Algebra / Linear

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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