Block Kronecker products and the vecb operator

A Note on the vec Operator Applied to Unbalanced Block-Structured Matrices

“…The vec of X is the sum of the vec operator applied to each of the component matrices in (2). A generic member of this set of component matrices can be written as in the following result.…”

“…Here, we consider the result of applying the vec operator to blockstructured matrices, including the case in which the blocks differ in size. Such a matrix is called unbalanced [2]. Previous studies of the vec operator and Kronecker product applied to block-structured matrices [2,3] have not addressed this problem.…”

“…Such a matrix is called unbalanced [2]. Previous studies of the vec operator and Kronecker product applied to block-structured matrices [2,3] have not addressed this problem.…”

Residual generator design for singular bilinear systems subjected to unmeasurable disturbances: an LMI approach

“…The right block Kronecker product (A B) is defined as follows (Koning et al, 1991) A B = Yu, D. and D.N. Shields (1996).…”

A variable step-size strategy for distributed estimation over adaptive networks

“…Also, using the bvec operator [27], we haveσ = bvec ¯ , where the bvec operator divides the matrix into smaller blocks and then applies the vec operator to each of the smaller blocks. Now, let R v = v I M denote the block diagonal noise covariance matrix for the entire network, where denotes the block Kronecker product [27] and v is a diagonal noise variance matrix for the network. Hence, the second term of the right-hand side of (25) is…”