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I still remember the following question on my linear algebra test in college: "Prove that A and A-Inverse have the same Eigen Values and corresponding Eigen Ve
by proee 17y ago
I still remember the following question on my linear algebra test in college:
"Prove that A and A-Inverse have the same Eigen Values and corresponding Eigen Vectors."
The solution to this made no sense, but I managed to memorize it so that I could pass the test.
Forest through the trees?
- jibiki 17y agoIt's not quite true, is it...? Av = cv v is an eigenvector, c the corresponding eigenvalue (A^-1)Av = (A^-1)cv v = c(A^-1)v (1/c)v = (A^-1)v So if c is an eigenvalue of A, then 1/c is an eigenvalue of (A^-1). (c can't be 0 because A is invertible, I think.)