A block diagonal matrix where every block is a Jordan block. Every complex square matrix is similar to a matrix in Jordan normal form. The geometric multiplicity of an eigenvalue λ‎ equals the number of Jordan blocks involving λ‎; the algebraic multiplicity of λ‎ is the sum of those block’s orders. The characteristic polynomial of the matrix is the product of all the block’s characteristic polynomials; the minimal polynomial of the matrix is the product of the each eigenvalue’s largest block’s characteristic polynomials. Two such matrices are:

Both matrices have characteristic polynomials (x−1)²(x−2)⁴; the minimal polynomials are (x−1)(x−2)⁴ and (x−1)(x−2)² respectively.