EAN: 9783031012679

SYNTHESIS LECTURES ON MATHEMATICS & STATISTICS ...

Jordan Canonical Form (JCF) is one of the most important  and useful  concepts in linear
algebra. In this book we develop JCF and show how to apply it to solving systems of
differential equations. We first develop JCF  including the concepts involved in it?eigenvalues
eigenvectors  and chains of generalized eigenvectors. We begin with the diagonalizable case and
then proceed to the general case  but we do not present a complete proof. Indeed  our interest
here is not in JCF per se  but in one of its important applications. We devote the bulk of our
attention in this book to showing how to apply JCF to solve systems of constant-coefficient
first order differential equations  where it is a very effective tool. We cover all
situations?homogeneous and inhomogeneous systems  real and complex eigenvalues. We also treat
the closely related topic of the matrix exponential. Our discussion is mostly confined to the
2-by-2 and 3-by-3 cases  and we present a wealth of examples that illustrate all the
possibilities in these cases (and of course  exercises for the reader). Table of Contents:
Jordan Canonical Form   Solving Systems of Linear Differential Equations   Background Results:
Bases  Coordinates  and Matrices   Properties of the Complex Exponential

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