|
libcats.org
Главная →
Jordan Canonical Form: Theory and Practice (Synthesis Lectures on Mathematics and Statistics)Jordan Canonical Form: Theory and Practice (Synthesis Lectures on Mathematics and Statistics)Steven Weintraub, Steven KrantzJordan Canonical Form (JCF) is one of the most important, and useful, concepts in linear algebra. The JCF of a linear transformation, or of a matrix, encodes all of the structural information about that linear transformation, or matrix. This book is a careful development of JCF. After beginning with background material, we introduce Jordan Canonical Form and related notions: eigenvalues, (generalized) eigenvectors, and the characteristic and minimum polynomials. We decide the question of diagonalizability, and prove the Cayley-Hamilton theorem. Then we present a careful and complete proof of the fundamental theorem: Let V be a finite-dimensional vector space over the field of complex numbers C, and let T : V - > V be a linear transformation. Then T has a Jordan Canonical Form. This theorem has an equivalent statement in terms of matrices: Let A be a square matrix with complex entries. Then A is similar to a matrix J in Jordan Canonical Form, i.e., there is an invertible matrix P and a matrix J in Jordan Canonical Form with A = PJP-1. We further present an algorithm to find P and J, assuming that one can factor the characteristic polynomial of A. In developing this algorithm we introduce the eigenstructure picture (ESP) of a matrix, a pictorial representation that makes JCF clear. The ESP of A determines J, and a refinement, the labeled eigenstructure picture (lESP) of A, determines P as well. We illustrate this algorithm with copious examples, and provide numerous exercises for the reader. Table of Contents: Fundamentals on Vector Spaces and Linear Transformations / The Structure of a Linear Transformation / An Algorithm for Jordan Canonical Form and Jordan Basis
Скачать книгу бесплатно (pdf, 504 Kb)
Читать «Jordan Canonical Form: Theory and Practice (Synthesis Lectures on Mathematics and Statistics)» EPUB | FB2 | MOBI | TXT | RTF
* Конвертация файла может нарушить форматирование оригинала. По-возможности скачивайте файл в оригинальном формате.
Популярные книги за неделю:
![]() Противостояние форматов DVD-R-RW и DVD+RWАвтор:Категория: Офисные программы бизнес-приложения
Размер книги: 56 Kb
![]() Тестирование Дот Ком, или Пособие по жестокому обращению с багами в интернет-стартапахАвтор: Роман Савин
Размер книги: 5.26 Mb
![]() Царство китайского языка - веселый путь овладения китайским языком. Учебник 2А и 2Б + аудиокурсАвтор: Liu Fuhua, Автор: Wang Wei, Автор: Zhou Ruian, Автор: Li Dongmei
Размер книги: 28.47 Mb
![]() Learning Curves: Body Image and Female Sexuality in Young Adult Literature (Scarecrow Studies in Young Adult Literature)Автор: Beth Younger
Размер книги: 5.55 Mb
Только что пользователи скачали эти книги:
![]() Diskret matematik och diskreta modeller (2nd printing)Автор: Kimmo Eriksson, Автор: Hillevi Gavel
Размер книги: 6.96 Mb
![]() Любовь в сетиАвтор: Епачинцева Наталья ВладимировнаКатегория: Современные любовные романы
Размер книги: 179 Kb
![]() A Companion to The Cantos of Ezra Pound: Vol. II (Cantos 74 - 120)Автор: Carroll F. Terrell
Размер книги: 15.07 Mb
![]() From Ancient Israel to Modern Judaism: Intellect in Quest of Understanding, Volume I: Essays in Honor of Marvin FoxАвтор: Jacob Neusner; Ernest S. Frerichs; Nahum M. Sarna
Размер книги: 9.75 Mb
![]() Η κινεζική σκέψηАвтор: Μαρσέλ Γκρανέ (Marcel Granet), Автор: Πωλίνα Λάμψα (μετάφραση)
Размер книги: 50.95 Mb
![]() Logical Empiricism and Pragmatism in EthicsАвтор: Cavell StanleyКатегория: fiction
Размер книги: 1.36 Mb
|
|