A square matrix of order n has n different eigenvalues, which is similar to a diagonal matrix () A. Sufficient and necessary condition B. sufficient but not necessary condition C. necessary but not sufficient condition D. neither sufficient nor necessary condition

A square matrix of order n has n different eigenvalues, which is similar to a diagonal matrix () A. Sufficient and necessary condition B. sufficient but not necessary condition C. necessary but not sufficient condition D. neither sufficient nor necessary condition

Sufficiency: n-order square matrix A has n different eigenvalues, assuming that the eigenvalues are: λ 1, λ 2 Therefore, the matrix A ~ λ 1 & nbsp; & nbsp; & nbsp; & nbsp; λ 2 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; λ n is similar to a diagonal matrix, then there may not be n different eigenvalues of a, and the eigenvalues may be equal, so B