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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?

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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?

(a) (F+λI)U=0

(b) (F-λI)U=0

(c) F-λI=0

(d) None of the mentioned

I got this question by my school principal while I was bunking the class.

The doubt is from State-Space System Analysis and Structures topic in section Discrete Time Systems Implementation of Digital Signal Processing

1 Answer

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The correct answer is (b) (F-λI)U=0

Explanation: 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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