December 2020
Intermediate to advanced
1064 pages
49h 13m
English
Content preview from Advanced Engineering Mathematics, 7th Edition
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8.12 Diagonalization
INTRODUCTION
In Chapter 10 we shall see that eigenvalues, eigenvectors, orthogonal matrices, and the topic of this present section, diagonalization, are important tools in the solution of systems of linear first-order differential equations. The basic question that we shall consider in this section is
For an n × n matrix A, can we find an n × n nonsingular matrix P such that P−1AP = D is a diagonal matrix?
A Special Notation
We begin by introducing a shorthand notation for the product of two n × n matrices. This notation will be useful in proving the principal theorem of this section. To illustrate, suppose A and B are ...
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