- #1
hkus10
- 50
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Let L : V>>>V be an invertible linear operator and let lambda be an eigenvalue of L with associated eigenvector x.
a) Show that 1/lambda is an eigenvalue of L^-1 with associated eigenvector x.
For this question, the things I know are that L is onto and one to one. Therefore, how to prove this question?
b) state the analogous statement for matrices. What does "state" the analogous statement mean?
Thanks
a) Show that 1/lambda is an eigenvalue of L^-1 with associated eigenvector x.
For this question, the things I know are that L is onto and one to one. Therefore, how to prove this question?
b) state the analogous statement for matrices. What does "state" the analogous statement mean?
Thanks