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A periodic matrix with period 1, so that A^2=A.

For two polynomials P_1(x)=a_mx^m+...+a_0 and P_2=b_nx^n+...+b_0 of degrees m and n, respectively, the Sylvester matrix is an (m+n)×(m+n) matrix formed by filling the matrix ...

A weighted adjacency matrix A_f of a simple graph is defined for a real positive symmetric function f(d_i,d_j) on the vertex degrees d_i of a graph as ...

Let A=a_(ij) be a matrix with positive coefficients and lambda_0 be the positive eigenvalue in the Frobenius theorem, then the n-1 eigenvalues lambda_j!=lambda_0 satisfy the ...

Fredholm's theorem states that, if A is an m×n matrix, then the orthogonal complement of the row space of A is the null space of A, and the orthogonal complement of the ...

The rank of a matrix or a linear transformation is the dimension of the image of the matrix or the linear transformation, corresponding to the number of linearly independent ...

Householder (1953) first considered the matrix that now bears his name in the first couple of pages of his book. A Householder matrix for a real vector v can be implemented ...

A block diagonal matrix, also called a diagonal block matrix, is a square diagonal matrix in which the diagonal elements are square matrices of any size (possibly even 1×1), ...

A symmetric matrix is a square matrix that satisfies A^(T)=A, (1) where A^(T) denotes the transpose, so a_(ij)=a_(ji). This also implies A^(-1)A^(T)=I, (2) where I is the ...

An augmented matrix is a matrix obtained by adjoining a row or column vector, or sometimes another matrix with the same vertical dimension. The most common use of an ...