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## Homework Statement

Prove or disprove: A and A

^{T}have the same eigenspaces.

## Homework Equations

## The Attempt at a Solution

I know that A and A

^{T}have the same determinant and so they have the same characteristic polynomial and eigenvalues, but then if they are transposed then the stuff above and below the main diagonal is swapped then they wouldn't have the same eigenspaces? Unless they were symmetric?