Let D be a non empty set, let us consider k, and let M be a matrix over D. Then M k is a matrix over D. We now state four propositions: (3) For every finite sequence M such that lenM = n+1 holds len(M n+1) = n: (4) Let M be a matrix over D of dimension n+1 m and M1 be a matrix over D. Then (i) if n > 0; then widthM = width(M n+1); and (ii) if M1 = hM(n+1)i; then widthM = widthM1: (5) For every ...

Stretching is a new sparse matrix method that makes matrices sparser by making them larger. Stretching has implications for computational complexity theory and applications in scientific and parallel computing. It changes matrix sparsity patterns to render linear equations more easily solved by parallel and sparse techniques. Some stretchings increase matrix condition numbers only moderately, a...

In this paper sufficient conditions are derived for the existence of unique and positive definite solutions of the matrix equations X−A1XA1− . . .−A∗mXAm = Q and X+A1XA1+ . . .+ A∗mXAm = Q. In the case there is a unique solution which is positive definite an explicit expression for this solution is given.

we present a model and propose an approach to compute an approximate solution of fully fuzzy linear system $(ffls)$ of equations in which all the components of the coefficient matrix are either nonnegative or nonpositive. first, in discussing an $ffls$ with a nonnegative coefficient matrix, we consider an equivalent $ffls$ by using an appropriate permutation to simplify fuzzy multiplications. t...