Low grade matrices and matrix fraction representations. Numerical Linear Algebra with Applications [1 citations — 0 self]
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by A. P. Mullhaupt, K. S. Riedel
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Abstract:
Abstract. The matrix equation MA = N is considered. The lgrade of a matrix A is the the largest rank of any subdiagonal block of a symmetric partition of a square matrix. When A has lgrade d, representation results are given for MA = N with M and N having lower bandwidth d. M can be chosen to be lower triangular or unitary. A second result is that if MA = N with M and N have lower bandwidths dM and dN then A = U + V with the lwidth(U) = dN \Gamma dM and U is an upper triangular matrix. 1.
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