Linear algebra
著者
書誌事項
Linear algebra
（Oxford science publications）
Oxford University Press, 1992
- hard
- pbk.
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注記
Includes indexes
内容説明・目次
- 巻冊次
-
pbk. ISBN 9780198534358
内容説明
Every student of mathematics needs a sound grounding in the techniques of linear algebra. It forms the basis of the study of linear equations, matrices, linear mappings, and differential equations, and comprises a central part of any course in mathematics. This textbook provides a rigorous introduction to the main concepts of linear algebra which should be suitable for all students coming to the subject for the first time. The book is in two parts: Part One develops the basic theory of vector spaces and linear maps, including demension, determinants, and eigenvalues and eigenvectors. Part Two goes on to develop more advanced topics and in particular the study of canonical forms for matrices. Professor Berberian is at pains to explain all the ideas underlying the proofs of results as well as to give numerous examples and applications. There is an abundant supply of exercises to reinforce the reader's grasp of the material and to elaborate on ideas from the text. As a result, this book should present a well-rounded and mathematically sound first course in linear algebra.
目次
- Part 1: Vector spaces
- linear mappings
- structure of vector spaces
- matrices
- inner product spaces
- determinants (2 x 2 and 3 x 3). Part 2: determinants (n x n)
- similarity (act 1)
- Euclidean spaces (spectral theorem)
- equivalence of matrices over a principal ideal ring
- similarity (act 2)
- unitary spaces
- tensor products. Appendicies: foundations
- integral domains, factorization
- Weierstrass-Bolzano theorem.
- 巻冊次
-
hard ISBN 9780198534365
内容説明
Every student of mathematics needs a sound grounding in the techniques of linear algebra. It forms the basis of the study of linear equations, matrices, linear mappings and differential equations, and comprises a central part of any course in mathematics. This textbook provides an introduction to the main concepts of linear algebra which should be suitable for students coming to the subject for the first time. The book is in two parts. Part 1 develops the basic theory of vector spaces and linear maps, including dimension, determinants, eigenvalues and eigenvectors. Part 2 goes on to examine more advanced topics and in particular the study of canonical forms for matrices.
目次
- PART I. Vector spaces
- Linear mappings
- Structure of vector spaces
- Matrices
- Inner product spaces
- Determinants (2x2 and 3x3)
- PART II. Determinants (nxn)
- Similarity (Act I)
- Euclidean spaces (spectral theorem)
- Equivalence of matrices over a principal ideal ring
- Similarity (Act II)
- Unitary spaces
- Tensor spaces.
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