---
tag: 08VRX3Q4PB
kind: concept
name: Semisimple endomorphism
msc: [15A04, 15A20]
sources:
  - url: https://en.wikipedia.org/wiki/Semisimple_operator
    locator: lead section
same_as:
  wikidata: Q3299281
  wikipedia: Semisimple operator
---

## Summary

An endomorphism of a finite-dimensional vector space is semisimple when each invariant subspace has an invariant complement.
Over an algebraically closed field, this means that it is diagonalisable.