Abstract Linear Algebra - Brossura

Curtis, Morton L.

Brossura

ISBN 10: 0387972633 ISBN 13: 9780387972633

Casa editrice: Springer, 2013

Riassunto

Intended for a first course on the subject, this text begins from scratch and develops the standard topics of Linear Algebra. Its progresses simply towards its ultimate goal, the Theorem of Hurwitz, which argues that the only normed algebras over the real numbers are the real numbers, the complex numbers, the quaternions, and the octonions. The book stresses the complete logical development of the subject.

Su questo libro

Contenuti:

0. Algebraic Preliminaries.- I. Vector Spaces and Linear Maps.- A. Vector Spaces.- B. Linear Maps.- C. Bases, Dimension.- D. Direct Sums, Quotients.- E. Eigenvectors and Eigenvalues (Part i).- F. Dual Spaces.- II. Matrices and Determinants.- A. Matrices.- B. Algebras.- C. Determinants, the Laplace Expansion.- D. Inverses, Systems of Equations.- E. Eigenvalues (Part ii).- III. Rings and Polynomials.- A. Rings.- B. Polynomials.- C. Cayley-Hamilton Theorem.- D. Spectral Theorems.- E. Jordan Form.- IV. Inner Product Spaces.- A. Rn as a Model, Bilinear Forms.- B. Real Inner Product Spaces, Normed Vector Spaces.- C. Complex Inner Product Spaces.- D. Orthogonal and Unitary Groups.- E. Stable Subspaces for Unitary and Orthogonal Groups.- V. Normed Algebras.- A. The Normed Algebras R and C.- B. Some General Results, Quaternions.- C. Alternative and Division Algebras.- D. Cayley-Dickson Process, Hurwitz Theorem.

Product Description:

Book by Curtis Morton L

Su questa edizione

• Editore: Springer
• Data di pubblicazione: 2013
• ISBN 10: 0387972633
• ISBN 13: 9780387972633
• Rilegatura: Copertina flessibile
• Numero di pagine: 184