MathDB
IMC 2002 Problem 11

Source: IMC 2002 Day 2 Problem 5

October 27, 2020
linear algebramatrixcomplex numbers

Problem Statement

Let AA be a complex n×nn \times n Matrix for n>1n >1. Let AHA^{H} be the conjugate transpose of AA. Prove that A⋅AH=InA\cdot A^{H} =I_{n} if and only if A=S⋅(SH)−1A=S\cdot (S^{H})^{-1} for some complex Matrix SS.
Back to ProblemsView on AoPS