Interpolation approach to the spectral resolution of square matrices (Q874761)

The author presents a proof of the spectral decomposition theorem for square matrices that are not necessarily diagonalizable, using properties of the basic Hermite interpolation polynomials. In particular he shows that the spectral decomposition of a square matrix \(A\) can be obtained in a simple way if one knows a nonzero polynomial \(w(z)\) such that \(w(A)=0.\)