Introduction to Matrix Theory矩陣?yán)碚撘?/p>
定 價：35 元
- 作者：趙迪 編著
- 出版時間：2014/4/1
- ISBN：9787512414938
- 出 版 社：北京航空航天大學(xué)出版社
- 中圖法分類：O151.2
- 頁碼：139
- 紙張：膠版紙
- 版次：1
- 開本：大16開
《矩陣?yán)碚撘摗酚衫罴t裔、趙迪編著。
《矩陣?yán)碚撘摗分v述了： This textbook contains six chapters, covering reviews on linear algebra; matrix functions;matrix decompositions such as singular value decompositions and spectral decompositions; generalized inverses;tensor product and nonnegative matrices. Each chapter includes many examples and problems to help students master the presented material.There are no prerequisites except for some basic knowledge on linear algebra. This book aims to provide the material for a basic matrix theory course to senior undergraduates or postgraduates in science and engineering, and can be used as a self- contained reference for a variety of readers.
李紅裔、趙迪編著的《矩陣?yán)碚撘摗菲赜诰仃嚴(yán)碚撝械挠?jì)算部分，重點(diǎn)闡述基本概念、具有重要應(yīng)用背景的定理公式，并提供了大量的算例來幫助讀者理解。本書共分六章，涵蓋了一般矩陣論課程所講述的內(nèi)容。具體包括矩陣范數(shù)、矩陣函數(shù)、矩陣分解（如QR分解、譜分解、滿秩分解、奇異值分解）、廣義矩陣逆、張量積、非負(fù)矩陣等。本書可作為工科高年級本科生或低年級研究生的矩陣論課程的教學(xué)用書。此外，本書也可作為相關(guān)領(lǐng)域科研工作者、工程開發(fā)人員等的參考資料。
Chapter 1 Introduction to Linear Algebra 1.1 The linear space 1.1.1 Fields and mappings 1.1.2 Definition of the linear space 1.1.3 Basis and dimension 1.1.4 Coordinate 1.1.5 Transformations of bases and coordinates 1.1.6 Subspace and the dimension theorem for vector spaces 1.2 Linear transformation and matrices 1.2.1 Linear transformation 1.2.2 Matrices of linear transformations and isomorphism 1.3 Eigenvalues and the Jordan canonical form 1.3.1 Eigenvalues and eigenvectors 1.3.2 Diagonal matrices 1.3.3 Schur's theorem and the Cayley- Hamilton theorem 1.3.4 The Jordan canonical form 1.4 Unitary spaces Exercise 1Chapter 2 Matrix Analysis 2.1 Vector norm 2.2 Matrix norm 2.3 Matrix sequences and series 2.4 Matrix function 2.5 Differentiation and integration of matrices 2.6 Applications of matrix functions 2.7 Estimation of eigenvalues Exercise 2Chapter 3 Matrix Decomposition 3.1 QR decomposition 3.2 Full rank decomposition 3.3 Singular value decomposition 3.4 The spectral decomposition Exercise 3Chapter 4 Generalized Inverse 4.1 The generalized inverse of a matrix 4.2 A{1},A{1,3} andA{1,4} 4.3 The Moore- Penrose inverse A+ 4.4 The generalized inverses and the linear equations Exercise 4Chapter 5 Tensor Product 5.1 Definition and properties of the tensor product 5.2 The tensor product and eigenvalues 5.3 Straighten operation on matrices 5.4 The tensor product and matrix equation Exercise 5Chapter 6 Introduction To Nonnegative Matrices 6.1 Preliminary properties on nonnegative matrices 6.2 Positive matrices and the Perron theorem 6.3 Irreducible nonnegative matrices 6.4 Primitive matrices and M matrices 6.5 Stochastic matrices 6.6 Two models of nonnegative matrices Exercise 6References
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