The vector is an eigenvector of the matrix. Every operator on a non-trivial complex finite dimensional vector space has an eigenvector, solving the invariant subspace problem for these spaces.

L. J. Ratliff, Jr., The Dimension of the Magic Square Vector Space, The American Mathematical Monthly, Vol. 66, No. 9 (Nov., 1959), pp. 793-795 ...

How Google Converted Language Translation Into a Problem of Vector Space Mathematics To translate one language into another, find the linear transformation that maps one to the other.