r columns and adding multiples of one row to another row. Singular value decomposition expresses any matrix A as a product UDV∗, where U and V are unitary matrices and D is a diagonal matrix.A matrix in Jordan normal form. The grey blocks are called Jordan blocks.The eigendecomposition or diagonalization expresses A as a product VDV−1, where D is a diagonal matrix and V is a suitable invertible matrix.[36]  If A can be written in this form, it is called diagonalizable. More generally, and applicable to all matrices, the Jordan decomposition transforms a matrix into Jordan normal form, that is to say matrices whose only nonzero entries are the eigenvalues λ1 to λn of A, placed on the main diagonal and possibly entries equal to one directly above the main diagonal, as shown at the right.[37]  Given the eigendecomposition, the nth power of A (i.e., n-fold iterated matrix multiplication) can be calculated viaAn = (VDV−1)n = VDV−1VDV−1...VDV−1 = VDnV−1and the power of a diagonal matri