Morton L. Curtis
Springer New York
1990e druk, 1990
9780387972633
Abstract Linear Algebra
Specificaties
Paperback, 168 blz.
|
Engels
Springer New York |
1990e druk, 1990
ISBN13: 9780387972633
Rubricering
Onderdeel van serie
Universitext
Levertijd ongeveer 8 werkdagen
Samenvatting
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.
Specificaties
ISBN13:9780387972633
Taal:Engels
Bindwijze:paperback
Aantal pagina's:168
Uitgever:Springer New York
Druk:1990
Serie:Universitext
Inhoudsopgave
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.