Page 61 - Introduction to Statistical Pattern Recognition

2 Random Vectors and their Properties 43

hl
I-- 0
I +h,
1
=I-- ' A. (2.159)
1 +h,

0 1

(2.160)

where A, =X-' and AMT =Z-'MMTE-' are obtained from (2. 01). If we
would like to calculateMT'S-'M in terms of MTC-'M,

(2.161)

(2.162)

Pseudoinverse: One way of calculating the pseudoinverse of a singular
square matrix is as follows. Let Q be a singular matrix with rank r, then Q can be
expressed by the eigenvalues and eigenvectors as

(2.163)

If we express Q * by

(2.164)

then