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Linear Algebra

Name: Linear Algebra
Brand: Springer, Berlin
SKU: 9789811669965
Price: 1120 CZK
Availability: InStock

From the Beginnings to the Jordan Normal Forms

Autor: Toshitsune Miyake

Jazyk:

Vazba: Brožovaná

Vydavatel: Springer, Berlin

Dostupnost: Skladem u dodavatele

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The purpose of this book is to explain linear algebra clearly for beginners. In doing so, the author...

Informace o knize

Autor

Toshitsune Miyake

Jazyk

Angličtina

Vazba

Kniha - Brožovaná

Vydáno

2023

Stránek

362

EAN

9789811669965

Enbook ID

43858507

Vydavatel

Springer, Berlin

Hmotnost

582

Rozměry

155 x 235

Kompletní popis

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.

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Linear Algebra

From the Beginnings to the Jordan Normal Forms

Informace o knize

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