LINEAR MAPS THAT PRESERVE PARTS OF THE SPECTRUM ON PAIRS OF SIMILAR MATRICES

In this paper, we characterize linear bijective maps f on the space of all n x n matrices over an algebraically closed field F having the property that the spectrum of f(A) and f(B) have at least one common eigenvalue for each similar matrices A and B. Using this result, we characterize linear bijective maps having the property that the spectrum of f(A) and f(B) have common elements for each matrices A and B having the same spectrum. As a corollary, we also characterize linear bijective maps preserving the equality of the spectrum.