《Abstract Linear Algebra》电子书下载

Abstract Linear Algebratxt,chm,pdf,epub,mobi下载
作者:Morton L. Curtis
出版社: Springer
出版年: 2013-10-4
页数: 184
定价: GBP 40.99
装帧: Paperback
ISBN: 9780387972633

内容简介 · · · · · ·

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 logica...

目录 · · · · · ·

Preface
Introduction
Chapter 0 -- Algebraic Preliminaries
Chapter I -- Vector Spaces and Linear Maps
A. Vector Spaces
B. Linear Maps
· · · · · ·()
Preface
Introduction
Chapter 0 -- Algebraic Preliminaries
Chapter 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
Chapter II -- Matrices and Determinants
A. Matrices
B. Algebras
C. Determinants, the Laplace Expansion
D. Inverses, Systems of Equations
E. Eigenvalues (Part ii)
Chapter III -- Rings and Polynomials
A. Rings
B. Polynomials
C. Cayley-Hamilton Theorem
D. Spectral Theorems
E. Jordan Form
Chapter IV -- Inner Product Spaces
A. R^n 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
Chapter 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
Bibliography
Index
· · · · · · ()

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