Question

This is an Advanced Linear Algebra Question.

Please answer only if your answer is fully sure.

Do not copy answers from online!!! Do not copy answers from online!!!

Prob 4. Let V be a finite-dimensional real vector space and let Te L(V). Define f : R R by f(A): dim range (T-AI) Which condition on T is equivalent to f being a continuous function? Hint: to be continuous f(A) is most likely to be a constant function since dimension would only return natural numbers. It's important to note that lambda is not restricted to being an eigenvalue. You should check to see what happens in both cases though (wink wink) think 1. Since the function is a constant function, what exactly that constant should be 2 In what cases might we fail to return that constant 3. Finally, how should we condition on T such that we could avoid the failing cases

Answer 1

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