A given translation-invariant quasifree Hamiltonian is ℛ-symmetric (i.e. [ R, H ] = 0 ) iff the coefficient matrix is restricted to be real.
When the sources and the mixing matrix are restricted to be non-negative, the problem can be seen as a non-negative matrix factorization (NMF) problem for which many algorithms have been developed[15].
In addition, the necessary condition for obtaining the optimal scale matrix is restricted to the diagonal matrix (e.g., Eq. (36)), where the off-diagonal elements are simply deleted in every iteration step thereby leading to solutions that do not ensure a true global minimum for the trace of the error matrix.
The Lp-class (p>0) of optimality criteria, which includes D-optimality, A-optimality and E-optimality as special cases, is considered in a regression setting where the experimental errors are uncorrelated with unequal variances and the design matrix is restricted to have row Euclidean norms bounded above by constants.
To keep the transmitted power unchanged after precoding, the precoder matrices are restricted as: mathsf{tr}left{mathbf{P}_{i}mathbf{R}_{x_{i}}mathbf{P}_{i}^{H}right}leq mathsf{tr}left{mathbf{R}_{x_{i}}right}, ; i=0,ldots,N-1, (16).
Initially, matrix-CGH was restricted to cell lines or investigated inherited diseases, both characterized by a genetically homogeneous cell population [ 4, 5].
The selection of matrices associated with specific tissue was restricted to breast tissue.
To our surprise, the distribution of these CSPG-associated structures was restricted overwhelmingly to the matrix compartment.
In normal liver, vitronectin was restricted to the stroma of portal tracts and to the subendothelial matrix of central veins.
It is shown how the estimation of such a matrix can be restricted to that of its corresponding coefficient matrix in the signal subspace, providing both performance enhancement and computational complexity reduction.
