Two matrices A and B are said to be unitarily equivalent if there exists a unitary matrix U such that B = U *AU. Two matrices which are unitarily equivalent are also similar.

What is meant by similar matrices?

Similar Matrices

The notion of matrices being ``similar'' is a lot like saying two matrices are row-equivalent. ... Definition (Similar Matrices) Suppose A and B are two square matrices of size n . Then A and B are similar if there exists a nonsingular matrix of size n , S , such that A=S−1BS A = S − 1 B S .

When is a matrix normal?

A matrix A is normal if and only if there exists a diagonal matrix Λ and a unitary matrix U such that A = UΛU^*. The diagonal entries of Λ are the eigenvalues of A, and the columns of U are the eigenvectors of A. The matching eigenvalues in Λ come in the same order as the eigenvectors are ordered as columns of U.