Linear Algebra : From the Beginnings to the Jordan Normal Forms (Record no. 34038)

000 -LEADER
fixed length control field a
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 250610b xxu||||| |||| 00| 0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9789811669934
082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 512.5
Item number MIY
100 ## - MAIN ENTRY--PERSONAL NAME
Personal name Miyake, Toshitsune
245 ## - TITLE STATEMENT
Title Linear Algebra : From the Beginnings to the Jordan Normal Forms
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Name of publisher, distributor, etc Springer,
Date of publication, distribution, etc 2022.
Place of publication, distribution, etc Singapore :
300 ## - PHYSICAL DESCRIPTION
Extent xvii, 361 p. ;
Other physical details ill. (some col.),
Dimensions 24 cm.
365 ## - TRADE PRICE
Price amount 49.99
Price type code
Unit of pricing 100.40
504 ## - BIBLIOGRAPHY, ETC. NOTE
Bibliography, etc Includes bibliographical references and index.
520 ## - SUMMARY, ETC.
Summary, etc The purpose of this book is to explain linear algebra clearly for beginners. In doing so, the author states and explains somewhat advanced topics such as Hermitian products and Jordan normal forms. Starting from the definition of matrices, it is made clear with examples that matrices and matrix operation are abstractions of tables and operations of tables. The author also maintains that systems of linear equations are the starting point of linear algebra, and linear algebra and linear equations are closely connected. The solutions to systems of linear equations are found by solving matrix equations in the row-reduction of matrices, equivalent to the Gauss elimination method of solving systems of linear equations. The row-reductions play important roles in calculation in this book. To calculate row-reductions of matrices, the matrices are arranged vertically, which is seldom seen but is convenient for calculation. Regular matrices and determinants of matrices are defined and explained. Furthermore, the resultants of polynomials are discussed as an application of determinants. Next, abstract vector spaces over a field K are defined. In the book, however, mainly vector spaces are considered over the real number field and the complex number field, in case readers are not familiar with abstract fields. Linear mappings and linear transformations of vector spaces and representation matrices of linear mappings are defined, and the characteristic polynomials and minimal polynomials are explained. The diagonalizations of linear transformations and square matrices are discussed, and inner products are defined on vector spaces over the real number field. Real symmetric matrices are considered as well, with discussion of quadratic forms. Next, there are definitions of Hermitian inner products. Hermitian transformations, unitary transformations, normal transformations and the spectral resolution of normal transformations and matrices are explained. The book ends with Jordan normal forms. It is shown that any transformations of vector spaces over the complex number field have matrices of Jordan normal forms as representation matrices
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Linear Algebra
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 Permanent location Current location Date acquired Source of acquisition Cost, normal purchase price Full call number Barcode Date last seen Koha item type
          DAU DAU 2025-05-26 KB 5019.00 512.5 MIY 035570 2025-06-10 Books

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