TABLE OF CONTENTS Some mathematical and matrix properties [HJ95] used throughout this book are summarized here.
Tr{ AB} = Tr{ BA}
det ( I + AB) = det ( I + BA)
Cauchy-Schwartz's inequality: 
Hadamard's inequality: 
of size n n
Fischer's inequality: 
if A, C square; equality occurs if B = 0
Weyl's inequality: for A and B n n hermitian matrices whose eigenvalues { ? k( A)} and ( ? k( B)} are sorted by decreasing order of magnitude
for k = 1, , n
for B full column rank
( A ? B) ? C = A ? ( B ? C)
( A ? B) H = A H ? B H
( A ? B)( C ? D) = ( AC ? BD)
( A ? B) -1 = A -1 ? B -1 if A, B square and non singular
det ( A m m ? B n n)= det ( A) n det ( B) m
Tr{ A ? B} = Tr{ A}Tr{ B}
with ? min( B) the smallest singular value of B
vec( ABC) = ( C T ? A)vec( B)
det ( I + ? A) = 1 +
