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For the sake of simplicity I'll give an example: Let A be a square real square matrix of order 4 and:

kerA = 3
rankA = 1
λ=1 is an eigenvalue

What can we know about its eigenvalues?

So far I've figured out 0 must be an eigenvalue since A is singular, but I'm struggling with its geometric and algebraic multiplicity.
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If the kerA = 3, then there are 3 linearly independent vectors that are eigenvectors with eigenvalue A (because Av=0v for all v in the kernel). So the geometric multiplicity of 0 is 3.
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