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 block-lower-triangular matrix is a matrix of the form where and are square matric...
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 ...
We also found that UX^⊥*AUY^⊥ is non-singular, so the right-hand side of (A.29), the block lower-triangular matrix on the left-hand side of (A.29), and accordingly, UY^A*A†UX^A are non-singular. Also, the determinant of (A.29) yields(A.30)|UA′*AUA″||UY^A*A†...
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 ...
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 ...
A square matrix A admits an inverse matrix if there is a matrix B such that AB=BA=I where I is the identity matrix. A matrix is invertible if and only if its determinant is nonzero. Working with determinant, we may need to use the following property ...
Answer to: Calculate the determinant coefficient and By signing up, you'll get thousands of step-by-step solutions to your homework questions. You...