東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Linear algebra = from the beginnings...

Miyake, Toshitsune.

FindBook

Google Book

Amazon

博客來

Linear algebra = from the beginnings to the Jordan normal forms /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Linear algebra/ by Toshitsune Miyake.
其他題名:	from the beginnings to the Jordan normal forms /
作者:	Miyake, Toshitsune.
出版者:	Singapore :Springer Nature Singapore : : 2022.,
面頁冊數:	xvii, 362 p. :ill. (some col.), digital ;24 cm.
內容註:	Preface -- 1. Matrices -- 2. Linear Equations -- 3. Determinants -- 4. Vector Spaces -- 5. Linear Mappings -- 6. Inner Product Spaces -- 7. Hermitian Inner Product Spaces -- 8. Jordan Normal Forms -- Notation -- Answers to Exercises -- References -- Index of Theorems -- Index.
Contained By:	Springer Nature eBook
標題:	Algebras, Linear. -
電子資源:	https://doi.org/10.1007/978-981-16-6994-1
ISBN:	9789811669941

Linear algebra = from the beginnings to the Jordan normal forms /
Miyake, Toshitsune.

Linear algebrafrom the beginnings to the Jordan normal forms /[electronic resource] :by Toshitsune Miyake. - Singapore :Springer Nature Singapore :2022. - xvii, 362 p. :ill. (some col.), digital ;24 cm.

Preface -- 1. Matrices -- 2. Linear Equations -- 3. Determinants -- 4. Vector Spaces -- 5. Linear Mappings -- 6. Inner Product Spaces -- 7. Hermitian Inner Product Spaces -- 8. Jordan Normal Forms -- Notation -- Answers to Exercises -- References -- Index of Theorems -- Index.

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.

ISBN: 9789811669941

Standard No.: 10.1007/978-981-16-6994-1doiSubjects--Topical Terms:

521915
Algebras, Linear.

LC Class. No.: QA184.2

Dewey Class. No.: 512.5

Linear algebra = from the beginnings to the Jordan normal forms /
LDR:03405nmm a2200313 a 4500 001 2303448
003 DE-He213
005 20220903214709.0
007 cr nn 008maaau
008 230409s2022 si s 0 eng d
020 $a 9789811669941 $q (electronic bk.)
020 $a 9789811669934 $q (paper)
024 7 $a 10.1007/978-981-16-6994-1 $2 doi
035 $a 978-981-16-6994-1
040 $a GP $c GP
041 0 $a eng
050 4 $a QA184.2
072 7 $a PBF $2 bicssc
072 7 $a MAT002050 $2 bisacsh
072 7 $a PBF $2 thema
082 0 4 $a 512.5 $2 23
090 $a QA184.2 $b .M685 2022
100 1 $a Miyake, Toshitsune. $3 3604742
245 1 0 $a Linear algebra $h [electronic resource] : $b from the beginnings to the Jordan normal forms / $c by Toshitsune Miyake.
260 $a Singapore : $b Springer Nature Singapore : $b Imprint: Springer, $c 2022.
300 $a xvii, 362 p. : $b ill. (some col.), digital ; $c 24 cm.
505 0 $a Preface -- 1. Matrices -- 2. Linear Equations -- 3. Determinants -- 4. Vector Spaces -- 5. Linear Mappings -- 6. Inner Product Spaces -- 7. Hermitian Inner Product Spaces -- 8. Jordan Normal Forms -- Notation -- Answers to Exercises -- References -- Index of Theorems -- Index.
520 $a 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 0 $a Algebras, Linear. $3 521915
650 1 4 $a Linear Algebra. $3 3338825
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-981-16-6994-1
950 $a Mathematics and Statistics (SpringerNature-11649)