Determinant of a block-triangular matrix A block-upper-triangular matrix is a matrix of the form where and are square matrices. PropositionLet be a block-upper-triangular matrix, as defined above. Then, Proof A
We try to design two numerical algorithms by a certain type of matrix reordering in matrix partition and another algorithm by using the transformation of a block upper triangular transformation for the cyclic heptadiagonal Toeplitz matrices. The cost of these algorithms is about 11n+O(logn) for ...
The largest index of any nonzero part of a partition in / is 1, and the largest value of such a part is 1. The two partitions in I that achieve this maximum are (11) and (21). To reduce M to block-triangular form, we subtract from the (11) and (21) rows appropriate ...
For upper triangular, lower triangular, or diagonal matrices, the value of the determinant will be the product of the diagonal elements.Answer and Explanation: Since the given information is that there are zeros below the diagonal, the matrix ...
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