Category: Sparse matrices

Shift matrix
In mathematics, a shift matrix is a binary matrix with ones only on the superdiagonal or subdiagonal, and zeroes elsewhere. A shift matrix U with ones on the superdiagonal is an upper shift matrix. Th
Block matrix
In mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices. Intuitively, a matrix interpreted as a block ma
Generalized permutation matrix
In mathematics, a generalized permutation matrix (or monomial matrix) is a matrix with the same nonzero pattern as a permutation matrix, i.e. there is exactly one nonzero entry in each row and each co
Bidiagonal matrix
In mathematics, a bidiagonal matrix is a banded matrix with non-zero entries along the main diagonal and either the diagonal above or the diagonal below. This means there are exactly two non-zero diag
Identity matrix
In linear algebra, the identity matrix of size is the square matrix with ones on the main diagonal and zeros elsewhere.
Nested dissection
In numerical analysis, nested dissection is a divide and conquer heuristic for the solution of sparse symmetric systems of linear equations based on graph partitioning. Nested dissection was introduce
Diagonal matrix
In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices. Elements of the main diagonal can either be ze
Pentadiagonal matrix
In linear algebra, a pentadiagonal matrix is a special case of band matrices.Its only nonzero entries are on the main diagonal, and the first two upper and two lower diagonals. So it is of the form It
Zero matrix
In mathematics, particularly linear algebra, a zero matrix or null matrix is a matrix all of whose entries are zero. It also serves as the additive identity of the additive group of matrices, and is d
Matrix unit
In linear algebra, a matrix unit is a matrix with only one nonzero entry with value 1. The matrix unit with a 1 in the ith row and jth column is denoted as . For example, the 3 by 3 matrix unit with i
Shear matrix
In mathematics, a shear matrix or transvection is an elementary matrix that represents the addition of a multiple of one row or column to another. Such a matrix may be derived by taking the identity m
Sparse matrix–vector multiplication
Sparse matrix–vector multiplication (SpMV) of the form y = Ax is a widely used computational kernel existing in many scientific applications. The input matrix A is sparse. The input vector x and the o
Cuthill–McKee algorithm
In numerical linear algebra, the Cuthill–McKee algorithm (CM), named after Elizabeth Cuthill and James McKee, is an algorithm to permute a sparse matrix that has a symmetric sparsity pattern into a ba
Anti-diagonal matrix
In mathematics, an anti-diagonal matrix is a square matrix where all the entries are zero except those on the diagonal going from the lower left corner to the upper right corner (↗), known as the anti
Sparse matrix
In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict definition regarding the proportion of zero-value
Skyline matrix
In scientific computing, skyline matrix storage, or SKS, or a variable band matrix storage, or envelope storage scheme is a form of a sparse matrix storage format matrix that reduces the storage requi
Band matrix
In mathematics, particularly matrix theory, a band matrix or banded matrix is a sparse matrix whose non-zero entries are confined to a diagonal band, comprising the main diagonal and zero or more diag
Tridiagonal matrix
In linear algebra, a tridiagonal matrix is a band matrix that has nonzero elements only on the main diagonal, the subdiagonal/lower diagonal (the first diagonal below this), and the supradiagonal/uppe
Reverse Cuthill-McKee algorithm
No description available.
Permutation matrix
In mathematics, particularly in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column and 0s elsewhere. Each such matrix, say P, rep
Heptadiagonal matrix
In linear algebra, a heptadiagonal matrix is a matrix that is nearly diagonal; to be exact, it is a matrix in which the only nonzero entries are on the main diagonal, and the first three diagonals abo