Beihang University press Chen Zuming, Zhou Jiasheng
Price:14.00 Filesize:37MB Pages:365
In modern mathematics, engineering technology, economic theory and management science, many related to matrix theory knowledge, therefore, one of the basic matrix theory of nature is the study and research of the discipline necessary. on the other hand, matrix theory development today, has formed a complete set of theory and method, the content is very rich, literature and monograph vast swimming.It must use the matrix knowledge to work in specialized in the field of science and technology and brings many difficulties, especially in engineering and technical personnel.This book is designed to set up a bridge to matrix theory for the various types of personnel, and through this bridge so that readers can as soon as possible to get the matrix knowledge they need.The greatest difficulty encountered book is probably material.Expect a suitable for a variety of professional teaching of course is not wise, is also the author of beyond the ability.Even if reluctantly to write out, I'm afraid the result is either a lengthy, or shaped like a dragonfly, is not caught.This of course is not expected.Therefore, we are compiling principle: outstanding key, high starting point, discusses in detail, contact the actual point.For the material properly we extensively solicit the relevant professional comrades.Experience with these comrades and the author for many years engaged in matrix theory teaching, at the same time, according to the State Education Commission on Engineering Master's graduate matrix theory teaching syllabus, the final selection of the elementary theory, linear matrix} space, matrix decomposition, matrix analysis, generalized inverse matrix and matrix as the basic content of straightened algorithm the book.We believe that these contents not only have basic theoretical significance in matrix theory, and has important application value.
Symbolic description introduction the first chapter the elementary matrix theory § 1.1 matrix and its elementary operations of 1. matrix and vector problem 1.12. block matrix multiplication with the elementary transformation of problem 1.2 § 1.2 determinant of a matrix and rank of matrix 1. determinant and its properties of exercises the rank of 1.32. matrix and its properties exercise 1.4 § 1.3 matrix the trace and eigenvalues of matrix 1. matrix trace and its elementary properties of 2. matrix characteristic value and calculation of 1.5 second exercises chapter on linear algebra based § 2.1 linear space 1. linear space definitions and examples of problem 2.12. subspace concept exercise 2.23. substrate and the dimension problem 2.34. and space with straight and the concept of space the generalization of § 2.2 inner product space 1. inner product space definitions and examples of problem 2.42. induced by the inner product geometric concept of 3. standard orthogonal basis and Gram-Schmidt exercise 2.5 § 2.3 linear transformation of 1. mapping and linear transformation exercise 2.62. linear transformation operations 2.73. exercises and linear transformation of the subspace exercise 2.8 § 2.4 linear transform matrix representation and emptyThe isomorphism between 1. linear transform matrix representation of 2. linear space isomorphic to problem 2.9 § 2.5 linear transformations of the simplest matrix representation of 1. linear transformation of the eigenvalues and eigenvectors of exercise 2.102. linear transformation of the zero polynomial and minimal polynomial of problem 2.11 3. is not diagonalizable linear transformation of the simplest matrix representation of . 2.12 third chapter matrices of several important decomposition § 3.1 matrix UR decomposition and its corollary 1. full rank matrix UR decomposition of 2. rectangular matrix decomposition of 3. 4. on several examples of full rank decomposition of matrix of several corollary § 3.2 Shure lemma and the normal matrix decomposition lemma 1. Shure 2. matrix singular value decomposition and the decomposition of exercise 3.1 § 3.3 idempotent matrix, projection operator and matrix spectral type 1. projection operator, idempotent operators and idempotent matrix 2. diagonalizable matrix spectral factorization 3.2 fourth exercises chapter generalized inverse of matrix § 4.1 More-Penrose generalized inverse matrix § 4.2 generalized inverse matrix A1. generalized inverse of the definition and structure of A 2. generalized inverse A properties of 3. generalized inverse A is applied to the solution of linear equations exercises
Theory: an introduction for graduate students of engineering majors matrix theory textbooks, matrix content includes: the elementary properties of matrix; linear algebra; matrix decomposition; generalized inverse matrix; matrix analysis as well as the Kronecker product of matrix and straightened algorithm.The introduction describes explain profound theories in simple language, clear matrix, and with a large number of exercises, so it can be used as a master's graduate students, but also can be used as a self-study books, but also can be used as engineering colleges for professional teachers reference.
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