what is the determinant of the identity matrix
Identity matrix The ith column of an identity matrix is the unit vector ei. It follows that the determinant of the identity matrix is 1 and the trace is n.
Hermitian matrix The diagonal elements must be real, as they must be their own complex conjugate.
Orthogonal matrix This leads to the equivalent characterization: a matrix Q is orthogonal if its transpose is equal to its inverse:
Diagonalizable matrix Note that the above examples show that the sum of diagonalizable matrices need not be diagonalizable.