Direct methods for sparse matrices
Direct methods for sparse matrices
Computing the block triangular form of a sparse matrix
ACM Transactions on Mathematical Software (TOMS)
An Implementation of Tarjan's Algorithm for the Block Triangularization of a Matrix
ACM Transactions on Mathematical Software (TOMS)
Sparse null bases and marriage theorems
Sparse null bases and marriage theorems
Strategies for Scaling and Pivoting for Sparse Symmetric Indefinite Problems
SIAM Journal on Matrix Analysis and Applications
Matching Theory (North-Holland mathematics studies)
Matching Theory (North-Holland mathematics studies)
| Hi-index | 0.00 |
We present some observations on the block triangular form (btf) of structurally symmetric, square, sparse matrices. If the matrix is structurally rank deficient, its canonical btf has at least one underdetermined and one overdetermined block. We prove that these blocks are transposes of each other. We further prove that the square block of the canonical btf, if present, has a special fine structure. These findings help us recover symmetry around the antidiagonal in the block triangular matrix. The uncovered symmetry helps us to permute the matrix in a special form which is symmetric along the main diagonal while exhibiting the blocks of the original btf. As the square block of the canonical btf has full structural rank, the observation relating to the square block applies to structurally nonsingular, square symmetric matrices as well.