The scalar 0 can be an eigenvalue of matrix square A. ✔Let M be an n x n matrix and let x be be a non-zero vector for which Mx = Xx for some scalar A. Then x is an eigenvector. The multiplicity of eigenvalue X of matrix A is the number of times A occurs as a root of the characteristic polynomial. Eigenvectors are never zero vectors. It is not possible to find the eigenvalues of upper triangular square matrix A. Similar matrices do not have the same eigenvalues. The determinant of (XIn — A) is the characteristic polynomial of matrix A.

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