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

882 APPENDIX D: BASIC MATRIX PROPERTIES AND OPERATIONS
D.3 Identity and Diagonal Matrices
An n x n square matrix is diagonal if all its off-diagonal entries are zero, that is,
D = diag (d1 , d 2 , ... , d n )
d1 0 0 0
0 d 2 0 0
0 0
0 dn - 1 0
0 d n
(D.7a)
(D.7b)
An identity matrix I n has unit diagonal entries
(D.8)
For an n x n square matrix A, if there exists a n x n square matrix B such that
BA = AB = I n
then
(D.9)
is the inverse matrix of A. For example, given a diagonal matrix
D
D = diag (d1 , d 2 , ... , d n )
-1 . ( 1 1 1 )
= diag
d1 ' d 2
' ... ' d n
D.4 Determinant of Square Matrices
The determinant of n x n square matrix A is defined recursively by
det (A) = I> i J(- l) i +iM;J
i=l
(D. 10)
where M;,; is an (n - 1) x (n - 1) matrix known as the minor of A by eliminating its ith row
and its jth column. Specifically, for a 2 x 2 matrix,
det [ ;
! ] = ad - be