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Synonym for (0,1)-matrix, binary matrix or Boolean matrix. Can be used to represent a k-adic relation. Markov matrix: A matrix of non-negative real numbers, such that the entries in each row sum to 1. Metzler matrix: A matrix whose off-diagonal entries are non-negative. Monomial matrix
Here is the conjugate transpose of V (or simply the transpose, if V contains real numbers only), and I denotes the identity matrix (of some dimension). Comment: The diagonal elements of D are called the singular values of A .
Others, such as matrix addition, scalar multiplication, matrix multiplication, and row operations involve operations on matrix entries and therefore require that matrix entries are numbers or belong to a field or a ring. [8] In this section, it is supposed that matrix entries belong to a fixed ring, which is typically a field of numbers.
The term echelon comes from the French échelon ("level" or step of a ladder), and refers to the fact that the nonzero entries of a matrix in row echelon form look like an inverted staircase. For square matrices , an upper triangular matrix with nonzero entries on the diagonal is in row echelon form, and a matrix in row echelon form is (weakly ...
The column space of a matrix is the image or range of the corresponding matrix transformation. Let be a field. The column space of an m × n matrix with components from is a linear subspace of the m-space. The dimension of the column space is called the rank of the matrix and is at most min(m, n). [1]
In particular, a tridiagonal matrix is a direct sum of p 1-by-1 and q 2-by-2 matrices such that p + q/2 = n — the dimension of the tridiagonal. Although a general tridiagonal matrix is not necessarily symmetric or Hermitian , many of those that arise when solving linear algebra problems have one of these properties.
Matrix multiplication completed in 2n-1 steps for two n×n matrices on a cross-wired mesh. There are a variety of algorithms for multiplication on meshes . For multiplication of two n × n on a standard two-dimensional mesh using the 2D Cannon's algorithm , one can complete the multiplication in 3 n -2 steps although this is reduced to half ...
If B is another linear map from the preceding vector space of dimension m, into a vector space of dimension p, it is represented by a matrix . A straightforward computation shows that the matrix of the composite map B ∘ A {\displaystyle B\circ A} is the matrix product B A . {\displaystyle \mathbf {BA} .}