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The rank of a matrix in Jordan canonical form
ossolalex
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Suppose that the rank of an n x n matrix in Jordan canonical form is less than or equal to n - 2. How can I show that it has at least two rows of zeros? How is it related to its Jordan blocks corresponding to zero eigenvalues?
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ossolalex
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Well, the kernel has dimension at least 2: what does that tell you about the zero eigenvalue?
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