A First Course in Linear Algebra · Problem MINM.T12
Matrices — Robert Beezer
Mathematics — Linear Algebra · unitary-matrices-inner-products
Problem
Suppose that we are checking if a square matrix of size n is unitary. Show that a straightforward application of Theorem CUMOS requires the computation of n2 inner products when the matrix is unitary, and fewer when the matrix is not orthogonal. Then show that this maximum number of inner products can be reduced to 21n(n+1) in light of Theorem IPAC.