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What is the condition to call a number λ is an Eigen value of F and a nonzero vector U is the associated Eigen vector?

What is the condition to call a number λ is an Eigen value of F and a nonzero vector U is the associated Eigen vector? Correct Answer (F-λI)U=0

A number λ is an Eigen value of F and a nonzero vector U is the associated Eigen vector if FU=λU Thus, we obtain (F-λI)U=0.

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