---
type: "problem"
title: "Endomorphism with all eigenvectors"
slug: "endomorphism-with-all-eigenvectors"
author: "ancient-tree"
tags: ["eigenvectors"]
difficulty: 10
qualityStatus: "unreviewed"
listed: true
origin: "Unknown"
originChapter: ""
originPage: ""
originNote: ""
license: "CC BY-SA 4.0"
---

Let $u$ be an [endomorphism](/concepts/endomorphism) of a vector space $E$ such that, for all $x$ in $E\backslash \{0\}$, $x$ is an eigenvector of $u$.

What is $u$ ?