Page 451 - Schaum's Outline of Theory and Problems of Signals and Systems

438 REVIEW OF MATRIX THEORY [APP. A

It can be easily verified by direct multiplication that if

then

Notes:

1. If the eigenvalues of A are A,, A,, . . . , A,, then the eigenvalues of An are A;, A;, . . .,A:.
2. Each eigenvector of A is still an eigenvector of An.
3. If P diagonalizes A, that is,

then it also diagonalizes An, that is,

since

B. Function of a Matrix:
Consider a function of A defined by