Abstract A computable criterion is given for two square matrices to possess a common eigenvector, as well as a criterion for one matrix to have an eigenvector lying in a given subspace. Some… Expand

Let be a complex matrix and let k be a fixed integer . If there exists a number such that for every subset having , then the rank of A is . Using this result (which is a generalization of a theorem… Expand

Abstract For an m × n matrix polynomial P, λ ϵ c is called an eigenvalue if there exists 0 ≠ x ϵ c n such that P(λ)x = 0. In this case x is an eigenvector of P corresponding to the eigenvalue λ. The… Expand