MathDB
Matrix equals its conjugate transpose

Source: 17th SEEMOUS 2023, Problem 3

March 9, 2023
linear algebramatrixSeemous

Problem Statement

Prove that if AA{} is an n×nn\times n matrix with complex entries such that A+A∗=A2A∗A+A^*=A^2A^* then A=A∗A=A^*. (Here, we denote by M∗M^* the conjugate transpose M‾t\overline{M}^t of the matrix MM{}).
Back to ProblemsView on AoPS