Band Matrix Representation of Triangular InputBalanced
نویسنده
چکیده
For generic lower triangular matrices, A, we prove that A ij = P d q=1 H iq G jq for i > j is equivalent to A = M ?1 N where M and N are d+1 banded matrices. A lower triangular matrix A is input balanced of order/rank d if there exists a rank-d matrix B such that AA = I ? BB. We prove that if A is triangular input balanced then generically, A = M ?1 N where M and N are d + 1 banded matrices. This also implies A i;j = P d q=1 H iq G jq for i > j. When B is a vector, explict representations are given and the eigendecomposition is evaluated.
منابع مشابه
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