Jordan Canonical Form by Steven H Weintraub
Jordan 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-
Fixed Point Theory from Early Foundations to Contemporary Challenges
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Descriptive Statistics for Scientists and Engineers
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Computational Calculus
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An Easy Path to Convex Analysis and Applications
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Monte Carlo Simulations Using Microsoft EXCEL
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Analysis of the Navier-Stokes Problem
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Geodesic Beams in Eigenfunction Analysis
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Calculus to Analysis
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Completely Regular Semigroup Varieties
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Dynamic Equations and Almost Periodic Fuzzy Functions on Time Scales
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The Linear Function and Euclidean Geometry
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Applied Stochastic Modeling
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Monte Carlo Methods
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Symmetry Analysis of Differential Equations
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Analysis of Epidemiologic Data Using R
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Survival Analysis
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An Introduction to Partial Differential Equations
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Boundary Value Problems
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The Fundamentals of Analysis for Talented Freshmen
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Continuous Distributions in Engineering and the Applied Sciences -- Part I
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The Integral
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Aspects of Differential Geometry V
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Probability and Statistics for STEM
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Time-Fractional Order Biological Systems with Uncertain Parameters
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Statistics is Easy
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Mathematical Problem Factories
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Discrete Distributions in Engineering and the Applied Sciences
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Fast Start Integral Calculus
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Numerical Integration of Space Fractional Partial Differential Equations
| SKU | Unavailable |
| ISBN 13 | 9783031012709 |
| ISBN 10 | 3031012704 |
| Title | Jordan Canonical Form |
| Author | Steven H Weintraub |
| Series | Synthesis Lectures On Mathematics And Statistics Ser |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Springer International Publishing AG |
| Year published | 2009-08-24 |
| Number of pages | 96 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |