Linear Algebra Done Right · Problem 5C.9

Eigenvalues, Eigenvectors, and Invariant Subspaces — Sheldon Axler

Mathematics — Linear Algebra · upper-triangular-matrices

Problem

Suppose

B

is a square matrix with complex entries. Prove that there exists an invertible square matrix

A

with complex entries such that

A^{-1}BA

is an upper-triangular matrix.