B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

884 APPENDIX D: BASIC MATRIX PROPERTIES AND OPERATIONS
Furthermore, the diagonal matrix
A = diag (A 1 A2 · · · An )
(D. 19)
consists of the corresponding eigenvalues of A.
Because
(D.20)
we can also write
(D.21)
The eigenvalues of A are very useful characteristics. In particular,
det (A) = n A;
i=l
n
Trace (A) =LA;
i= l
(D.22a)
(D.22b)
D. 7 Special Hermitian Square Matrices
Let an n x n matrix A be Hermitian. A is positive definite if for any n x 1 vector x i= 0, we
have
A is semipositive definite if for any n x 1 vector x, we have
A is negative definite if for any n x 1 vector x -1- 0, we have
A is positive definite if and only if all its eigenvalues are positive.
(D.23)
(D.24)
(D.25)