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The conjugate gradient method can be viewed as a special variant of the Lanczos method for positive definite symmetric systems. The minimal residual method (MINRES) and ...

A generalized eigenvector for an n×n matrix A is a vector v for which (A-lambdaI)^kv=0 for some positive integer k in Z^+. Here, I denotes the n×n identity matrix. The ...

The algebraic connectivity of a graph is the numerically second smallest eigenvalue (counting multiple eigenvalues separately) of the Laplacian matrix of a graph G. In other ...

The Gershgorin circle theorem (where "Gershgorin" is sometimes also spelled "Gersgorin" or "Gerschgorin") identifies a region in the complex plane that contains all the ...

Let V be a real symmetric matrix of large order N having random elements v_(ij) that for i<=j are independently distributed with equal densities, equal second moments m^2, ...

Given a matrix A, a Jordan basis satisfies Ab_(i,1)=lambda_ib_(i,1) and Ab_(i,j)=lambda_ib_(i,j)+b_(i,j-1), and provides the means by which any complex matrix A can be ...

The ABC (atom-bond connectivity) spectral radius rho_(ABC) of a graph is defined as the largest eigenvalue of its ABC matrix. Chen (2019) showed that for a tree on 3 or more ...

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

For any nonzero lambda in C, either 1. The equation Tv-lambdav=0 has a nonzero solution v, or 2. The equation Tv-lambdav=f has a unique solution v for any function f. In the ...

The Randić spectral radius rho_(Randic) of a graph is defined as the largest eigenvalue of its Randić matrix.