Answer to Question #224240 in Linear Algebra for Dhananjay

Question

Can 2 be a entry of a unitary matrix? Answer with reason.

Answer 1

No, all entries must have an absolute value less than 1.

If a unary matrix U has in entries u_ij then the i^th diagonal elements of the product U U^* is u_i1*u_i1^*+ u_i2*u_i^* + ... + u_iN*u_iN^* = |u_i1|² +|u_i2|² + ... |u_iN|² = 1. So |u_ij|² should be less or equal to 1 for each i and j.