Matrices and Linear Transformations: Second Edition
Undergraduate-level introduction to linear algebra and matrix theory. Explores matrices and linear systems, vector spaces, determinants, spectral decomposition, Jordan canonical form, much more. Over 375 problems. Selected answers. 1972 edition.
Read More ↓Title Statements
- Full title :Matrices and Linear Transformations : Second Edition.
Summary
Undergraduate-level introduction to linear algebra and matrix theory. Explores matrices and linear systems, vector spaces, determinants, spectral decomposition, Jordan canonical form, much more. Over 375 problems. Selected answers. 1972 edition.
Read More ↓Edition Statements
- Publication Date:©2012.
- Edition:2nd ed
Publication Statements
- Publisher(s):Dover Publications
- Place of Publication:New York
- Language:eng
- Publication Date:©2012.
Notes
27345072.
The Physical Object
- Description:1 online resource (542 pages).
Edition Identifiers
- ISBN:9780486132419, 0486132412
- oclc:on1113477865
- LC Classification:QA188 .C85 2014
- Dewey Decimal:512.9/434
Table of Contents
Cover -- Title Page -- Copyright Page -- Contents -- Chapter 1 Matrices and Linear Systems -- 1.1 Introduction -- 1.2 Fields and number systems -- 1.3 Matrices -- 1.4 Matrix addition and scalar multiplication -- 1.5 Transposition -- 1.6 Partitioned matrices -- 1.7 Special kinds of matrices -- 1.8 Row equivalence -- 1.9 Elementary matrices and matrix inverses -- 1.10 Column equivalence -- 1.11 Equivalence -- Chapter 2 Vector Spaces -- 2.1 Introduction -- 2.2 Subspaces -- 2.3 Linear independence and bases -- 2.4 The rank of a matrix -- 2.5 Coordinates and isomorphisms -- 2.6 Uniqueness theorem for row equivalence -- Chapter 3 Determinants -- 3.1 Definition of the determinant -- 3.2 The Laplace expansion -- 3.3 Adjoints and inverses -- 3.4 Determinants and rank -- Chapter 4 Linear Transformations -- 4.1 Definition and examples -- 4.2 Matrix representation -- 4.3 Products and inverses -- 4.4 Change of basis and similarity -- 4.5 Characteristic vectors and characteristic values -- 4.6 Orthogonality and length -- 4.7 Gram-Schmidt process -- 4.8 Schur's theorem and normal matrices -- Chapter 5 Similarity: Part I -- 5.1 The Cayley-Hamilton theorem -- 5.2 Direct sums and invariant subspace…
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