Description

by
H. E. Rose (Author),
Harvey E. Rose (Author)

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.

Number of Pages: 268Dimensions: 0.63 x 9.21 x 6.14 INIllustrated: YesPublication Date: October 03, 2002