# Multiplicities and eigenvalues

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Suppose A and B are similar matrices, and that μ is an eigenvalue of A. We know that μ is also an eigenvalue of B, with the same algebraic multiplicity. Suppose that g is the geometric multiplicity of μ, as an eigenvalue of B. Show that μ has geometric multiplicity g as an eigenvalue of A.

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Proof:

Since and are similar matrices, then we can find an invertible matrix , such that . Suppose is an eigenvalue of with geometric multiplicity ...

#### Solution Summary

This provides an example of working with geometric multiplicities and eigenvalues.

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