Page 72 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition
P. 72
Let A and be as in Example 7; that is,
Then
Polynomial Expressions Involving Matrices
If A is a square matrix, say , and if
is any polynomial, then we define (1)
matrix that results when A is substituted for x in 1 and is
where I is the identity matrix. In words, is the
replaced by .
EXAMPLE 9 Matrix Polynomial
If
then
Properties of the Transpose
The next theorem lists the main properties of the transpose operation.
THEOREM 1.4.9
Properties of the Transpose
If the sizes of the matrices are such that the stated operations can be performed, then
(a)
