|, // denotes the vertical bar for "given"
M denotes [scalar, vector, matrix]
M_T denotes transpose of M, also transpose(M
|M| , //M// denotes absolute value of matrix M (each element)
||M||, ////M//// denotes spectral norm of M ////M////2
M_bar denotes an overscore on M
M_tilde denotes a tilde over a Matrix symbol
|x|, //x// is the absolute value vector of x, |x| = (|x1|, |x2|, . . . , |xn|)T
||x||2 is the vector norm of x, ||x||2 = √Σni=1 |xi|2
I is the identity matrix
M > (≥)0 means M is a positive definite(semidefinite)matrix
M > (≥)B means M − B is a positive definite(semidefinite)matrix
M ≽ 0 means M is a positive(nonnegative) matrix, i.e, mij ≥ 0,
M ≽ B means the elements of matrices M,B satisfy the inequality mij ≥ bij
|M| is the absolute value matrix of M; |M| = (|mij |)nÃ—n
(M) is spectral radius of M
λmax(M) means the maximum eigenvalue of matrix M
λmin(M) means the minimum eigenvalue of matrix M
ρ(M) is the spectral radium of matrix M
||M||2 is the spectral norm of matrix M. ||M||2 = √λmax(MTM)
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Kronecker product - If A is an m n matrix and B is a p q matrix, then the Kronecker product A ⊗ B is the mp nq block matrix:
a11*B ... a1n*B
A ⊗ B = . ... .
a1n*B ... ann*B