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Let A be a matrix with the elementary divisors of its characteristic matrix expressed as powers of its irreducible polynomials in the field F[lambda], and consider an ...

The arithmetic-geometric spectral radius rho_(AG) of a graph is defined as the largest eigenvalue of its arithmetic-geometric matrix.

Let |z| be a vector norm of a vector z such that ||A||=max_(|z|=1)||Az||. Then ||A|| is a matrix norm which is said to be the natural norm induced (or subordinate) to the ...

Rodrigues' rotation formula gives an efficient method for computing the rotation matrix R in SO(3) corresponding to a rotation by an angle theta about a fixed axis specified ...

A graph in which each graph edge is replaced by a directed graph edge, also called a digraph. A directed graph having no multiple edges or loops (corresponding to a binary ...

The kth power of a graph G is a graph with the same set of vertices as G and an edge between two vertices iff there is a path of length at most k between them (Skiena 1990, ...

The Randić index of a graph is defined as half the sum of the matrix elements of its Randić matrix. While the index was introduced to model the branching of the carbon-atom ...

The Sherman-Morrison formula is a formula that allows a perturbed matrix to be computed for a change to a given matrix A. If the change can be written in the form u tensor v ...

The order ideal in Lambda, the ring of integral laurent polynomials, associated with an Alexander matrix for a knot K. Any generator of a principal Alexander ideal is called ...

Two or more functions, equations, or vectors f_1, f_2, ..., which are not linearly dependent, i.e., cannot be expressed in the form a_1f_1+a_2f_2+...+a_nf_n=0 with a_1, a_2, ...