Advanced linear algebra (Record no. 202333)

000 -LEADER
fixed length control field 03437 a2200193 4500
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 160203b2016 xxu||||| |||| 00| 0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9781498754033
082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER
Item number W6A2
Classification number 512.5
100 ## - MAIN ENTRY--PERSONAL NAME
Personal name Woerdeman, Hugo J.
9 (RLIN) 328404
245 ## - TITLE STATEMENT
Title Advanced linear algebra
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Place of publication, distribution, etc Boca Raton
Name of publisher, distributor, etc CRC Press
Date of publication, distribution, etc 2016
300 ## - PHYSICAL DESCRIPTION
Extent xix, 327 p.
440 ## - SERIES STATEMENT/ADDED ENTRY--TITLE
Title Textbooks in Mathematics
9 (RLIN) 328405
504 ## - BIBLIOGRAPHY, ETC. NOTE
Bibliography, etc Table of Contents:

1. Fields and Matrix Algebra

The Field Z3
The Field Axioms
Field Examples
Matrix Algebra over Different Fields
Exercises

2. Vector Spaces

Definition of a Vector Space
Vector Spaces of Functions
Subspaces and More Examples of Vector Spaces
Linear Independence, Span, and Basis
Coordinate Systems
Exercises

3. Linear Transformations

Definition of a Linear Transformation
Range and Kernel of Linear Transformations
Matrix Representations of Linear Maps
Exercises

4. The Jordan Canonical Form

The Cayley-Hamilton Theorem
Jordan Canonical Form for Nilpotent Matrices
An Intermezzo about Polynomials
The Jordan Canonical Form
The Minimal Polynomial
Commuting Matrices
Systems of Linear Differential Equations
Functions of Matrices
The Resolvent
Exercises

5. Inner Product and Normed Vector Spaces

Inner Products and Norms
Orthogonal and Orthonormal Sets and Bases
The Adjoint of a Linear Map
Unitary Matrices, QR, and Schur Triangularization
Normal and Hermitian Matrices
Singular Value Decomposition
Exercises

6. Constructing New Vector Spaces from Given Ones

The Cartesian Product
The Quotient Space
The Dual Space
Multilinear Maps and Functionals
The Tensor Product
Anti-Symmetric and Symmetric Tensors
Exercises

7. How to Use Linear Algebra

Matrices You Can't Write Down, but Would Still Like to Use
Algorithms Based on Matrix Vector Products
Why Use Matrices When Computing Roots of Polynomials?
How to Find Functions with Linear Algebra?
How to Deal with Incomplete Matrices
Solving Millennium Prize Problems with Linear Algebra
How Secure Is RSA Encryption?
Quantum Computation and Positive Maps
Exercises

How to Start Your Own Research Project

Answers to Exercises


520 ## - SUMMARY, ETC.
Summary, etc Advanced Linear Algebra features a student-friendly approach to the theory of linear algebra. The author’s emphasis on vector spaces over general fields, with corresponding current applications, sets the book apart. He focuses on finite fields and complex numbers, and discusses matrix algebra over these fields. The text then proceeds to cover vector spaces in depth. Also discussed are standard topics in linear algebra including linear transformations, Jordan canonical form, inner product spaces, spectral theory, and, as supplementary topics, dual spaces, quotient spaces, and tensor products.

Written in clear and concise language, the text sticks to the development of linear algebra without excessively addressing applications. A unique chapter on "How to Use Linear Algebra" is offered after the theory is presented. In addition, students are given pointers on how to start a research project. The proofs are clear and complete and the exercises are well designed. In addition, full solutions are included for almost all exercises.


(https://www.crcpress.com/Advanced-Linear-Algebra/Woerdeman/9781498754033)
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Algebras, Linear
9 (RLIN) 328575
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Cayley algebra
9 (RLIN) 328576
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Source of classification or shelving scheme
Item type Books
Holdings
Withdrawn status Lost status Source of classification or shelving scheme Damaged status Not for loan Collection code Permanent location Current location Shelving location Date acquired Source of acquisition Cost, normal purchase price Item location Full call number Barcode Date last seen Cost, replacement price Koha item type
          Non-fiction Vikram Sarabhai Library Vikram Sarabhai Library   2016-02-01 Pustak 4899.00 Slot 1364 (0 Floor, East Wing) 512.5 W6A2 190938 2016-02-01 6123.74 Books

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