Low Grade Matrices and Matrix Fraction Representaions
نویسنده
چکیده
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 d M and d N then A = U + V with the lwidth(U) = d N ? d M and U is an upper triangular matrix.
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The lgrade of a n × n matrix A is the largest rank of any subdiagonal block of a symmetric partition of A. A number of algebraic results on lgrade are given. When A has lgrade d, it can be be approximately decomposed as A = U + V , where U is an upper triangular matrix and V has rank d. If A satisfies GA = N with G and N have lower bandwidths dG and dN , then the decomposition is exact: A = U +...
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تاریخ انتشار 2007