Matrix Theory : From Generalized Inverses to Jordan Form

丛 书 名：Pure and Applied Mathematics, A Series of Monographs and Textbooks

版本说明：1

作     者：Piziak, Robert 

I S B N：(纸本) 9781584886259 

出 版 社：CRC Press 

出 版 年：2007年

主 题 词：mathematics \u0026 statistics 

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 070101[理学-基础数学] 

馆 藏 号：201109640...

摘      要：In 1990, the National Science Foundation recommended that every college mathematics curriculum should include a second course in linear algebra. In answer to this recommendation, Matrix Theory: From Generalized Inverses to Jordan Form provides the material for a second semester of linear algebra that probes introductory linear algebra concepts while also exploring topics not typically covered in a sophomore-level *** the material to advanced undergraduate and beginning graduate students, the authors offer instructors flexibility in choosing topics from the book. The text first focuses on the central problem of linear algebra: solving systems of linear equations. It then discusses LU factorization, derives Sylvester s rank formula, introduces full-rank factorization, and describes generalized inverses. After discussions on norms, QR factorization, and orthogonality, the authors prove the important spectral theorem. They also highlight the primary decomposition theorem, Schur s triangularization theorem, singular value decomposition, and the Jordan canonical form theorem. The book concludes with a chapter on multilinear *** this classroom-tested text students can delve into elementary linear algebra ideas at a deeper level and prepare for further study in matrix theory and abstract algebra.