Suppose V is finite-dimensional, T belongs to End(V) and lambda in F . Then the
following are equivalent:
(a) lambda is an eigenvalue of T ;
(b) T -lambdaI is not injective;
1
Expert's answer
2020-06-11T20:49:05-0400
"\\lambda" is an Eigenvalue of matrrix T iff "(T-\\lambda I)X=0" for some non-zero X.
"\\iff X\\in ker\\{T-\\lambda I \\} \\iff T-\\lambda I" is not injective.
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