If $ A\in \textrm{M}_4(\mathbb{R})$ and it has eigen values $0,-i,i$. Can I determine the algebraic multiplities from this? My gut is telling me that $0$ must have multiplity 2 and the others 1. Perhaps something to do with the Fundemental Theorem of Algebra as well as a complex root implies complex conjugate roots as well. However this is a vague argument. Can someone help?
2026-03-30 13:20:12.1774876812
Can I determine the algebraic multiplities from eigen values $0,-i,i$?
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