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Published by Berlin. Springer Verlag., 1989
ISBN 10: 3540502688 ISBN 13: 9783540502685
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Published by Springer, Berlin|Springer Nature Singapore|Springer, 2023
ISBN 10: 9811669961 ISBN 13: 9789811669965
Seller: moluna, Greven, Germany
Condition: New. 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 .
Language: English
Published by Springer-Verlag, Berlin, 1989
ISBN 10: 3540502688 ISBN 13: 9783540502685
First Edition
Hardcover. Condition: Very Good endpaper. Dust Jacket Condition: No Dust Jacket. 1st. Spine fading. Previous owner's name front; 8vo; 335 pages.
Language: English
Published by Springer Nature Singapore, Springer Nature Singapore Sep 2022, 2022
ISBN 10: 9811669937 ISBN 13: 9789811669934
Seller: buchversandmimpf2000, Emtmannsberg, BAYE, Germany
Buch. Condition: Neu. Neuware -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 withJordan 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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 380 pp. Englisch.
Language: English
Published by Springer Nature Singapore, Springer Nature Singapore Sep 2023, 2023
ISBN 10: 9811669961 ISBN 13: 9789811669965
Seller: buchversandmimpf2000, Emtmannsberg, BAYE, Germany
Taschenbuch. Condition: Neu. Neuware -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 withJordan 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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 380 pp. Englisch.