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Eigenvalues are a special set of scalars associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic roots, ...

The eigenvalues of a graph are defined as the eigenvalues of its adjacency matrix. The set of eigenvalues of a graph is called a graph spectrum. The largest eigenvalue ...

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 ...

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 ...

If L^~ is a linear operator on a function space, then f is an eigenfunction for L^~ and lambda is the associated eigenvalue whenever L^~f=lambdaf. Renteln and Dundes (2005) ...

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, ...

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.