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Let ||A|| be the matrix norm associated with the matrix A and |x| be the vector norm associated with a vector x. Let the product Ax be defined, then ||A|| and |x| are said to ...

An n×n square matrix M with M_(ii) = 1 (1) M_(ij) = M_(ji)>1 (2) for all i,j=1, ..., n.

A diagonal of a square matrix which is traversed in the "southeast" direction. "The" diagonal (or "main diagonal," or "principal diagonal," or "leading diagonal") of an n×n ...

If A is an n×n square matrix and lambda is an eigenvalue of A, then the union of the zero vector 0 and the set of all eigenvectors corresponding to eigenvalues lambda is ...

Let A=a_(ij) be a matrix with positive coefficients so that a_(ij)>0 for all i,j=1, 2, ..., n, then A has a positive eigenvalue lambda_0, and all its eigenvalues lie on the ...

Given a set V of m vectors (points in R^n), the Gram matrix G is the matrix of all possible inner products of V, i.e., g_(ij)=v_i^(T)v_j. where A^(T) denotes the transpose. ...

Every complex matrix can be broken into a Hermitian part A_H=1/2(A+A^(H)) (i.e., A_H is a Hermitian matrix) and an antihermitian part A_(AH)=1/2(A-A^(H)) (i.e., A_(AH) is an ...

A generalization of the matrix to an n_1×n_2×... array of numbers.

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

An n×n complex matrix A is called indefinite if nonzero vectors x and y exist such that x^*Ax>0>y^*Ay, where x^* denotes the conjugate transpose. A matrix m may be tested to ...