MathDB

IMC 2001 Problem 5

Source: IMC 2001 Day 1 Problem 5

October 30, 2020

linear algebramatrix

Problem Statement

Let

A

be an

n\times n

complex matrix such that

A \ne \lambda I_{n}

for all

\lambda \in \mathbb{C}

. Prove that

A

is similar to a matrix having at most one non-zero entry on the maindiagonal.