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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 ...

Let A be an n×n matrix with complex or real elements with eigenvalues lambda_1, ..., lambda_n. Then the spectral radius rho(A) of A is rho(A)=max_(1<=i<=n)|lambda_i|, i.e., ...

A nonempty finite set of n×n integer matrices for which there exists some product of the matrices in the set which is equal to the zero matrix.

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 ...

The square root method is an algorithm which solves the matrix equation Au=g (1) for u, with A a p×p symmetric matrix and g a given vector. Convert A to a triangular matrix ...

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 ...