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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 bounded operator T:V->W between two Banach spaces satisfies the inequality ||Tv||<=C||v||, (1) where C is a constant independent of the choice of v in V. The inequality is ...

Chió pivotal condensation is a method for evaluating an n×n determinant in terms of (n-1)×(n-1) determinants. It also leads to some remarkable determinant identities (Eves ...

A graph G is said to be disconnected if it is not connected, i.e., if there exist two nodes in G such that no path in G has those nodes as endpoints. The numbers of ...

A Hessenberg matrix is a matrix of the form [a_(11) a_(12) a_(13) ... a_(1(n-1)) a_(1n); a_(21) a_(22) a_(23) ... a_(2(n-1)) a_(2n); 0 a_(32) a_(33) ... a_(3(n-1)) a_(3n); 0 ...

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 matrix used in the Jacobi transformation method of diagonalizing matrices. The Jacobi rotation matrix P_(pq) contains 1s along the diagonal, except for the two elements ...

A method of matrix diagonalization using Jacobi rotation matrices P_(pq). It consists of a sequence of orthogonal similarity transformations of the form ...

The Jordan canonical form, also called the classical canonical form, of a special type of block matrix in which each block consists of Jordan blocks with possibly differing ...

Given an m×n matrix A and a p×q matrix B, their Kronecker product C=A tensor B, also called their matrix direct product, is an (mp)×(nq) matrix with elements defined by ...