Every eigenvalue of a unitary matrix has absolute value 1. I was wondering whether a matrix whose eigenvalues all have absolute value 1 must be unitary?
Thanks!
Every eigenvalue of a unitary matrix has absolute value 1. I was wondering whether a matrix whose eigenvalues all have absolute value 1 must be unitary?
Thanks!
2: Yes, if the algebraic multiplicity of all eigenvectors equal their geometric multiplicity, then the matrix is diagonalisable because the dimensions of the eigenspaces add up to $n$ so that you can choose $n$ linear independent eigenvectors (at least over an algebraically closed field)