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Also known as "Laplacian" determinant expansion by minors, expansion by minors is a technique for computing the determinant of a given square matrix M. Although efficient for ...

The idiosyncratic polynomial is the bivariate graph polynomial defined as the characteristic polynomial in x of A+y(J-I-A), where A is the adjacency matrix, J is the unit ...

The characteristic equation is the equation which is solved to find a matrix's eigenvalues, also called the characteristic polynomial. For a general k×k matrix A, the ...

A rewriting of a given quantity (e.g., a matrix) in terms of a combination of "simpler" quantities.

A fixed point for which the stability matrix has both eigenvalues negative, so lambda_1<lambda_2<0.

A fixed point for which the stability matrix has both eigenvalues positive, so lambda_1>lambda_2>0.

The symmetric successive overrelaxation (SSOR) method combines two successive overrelaxation method (SOR) sweeps together in such a way that the resulting iteration matrix is ...

The natural norm induced by the L1-norm is called the maximum absolute column sum norm and is defined by ||A||_1=max_(j)sum_(i=1)^n|a_(ij)| for a matrix A. This matrix norm ...

Sylvester's criterion states that a matrix M is positive definite iff the determinants associated with all upper-left submatrices of M are positive.

Given a square matrix M, the following are equivalent: 1. |M|!=0. 2. The columns of M are linearly independent. 3. The rows of M are linearly independent. 4. Range(M) = R^n. ...