Page 183 - Introduction to Statistical Pattern Recognition
P. 183
4 Parametric Classifiers 165
where
R, = (4.134)
R,. = (4.135)
Many properties of the block toeplitz matrix are known, and listed as fol-
lows without proof [6].
(1) A @B#A @B, (4.136)
(2) (A @B)(C @D) = AC @BD , (4.137)
(3) (A @B)' =AT @BT, (4.138)
(4) (A @B)-' =A-' C3B-I , (4.139)
(5) tr(A @B) = (tr A)(tr B) , (4.140)
(6) (A @B)(@ BY) = (a @")(A @ p) (4.141)
where A0 =@A and BY = Yp
e, Y: eigenvector matrices of A and B
A, p: eigenvalue matrices of A and B,
(7) IA @Bl = IAIml~I"= IAImlBI" (4.142)
where A and B are nxn and mxm matrices.
