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March 25, 2017

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V = Mnxn is a space vector formed by all the square matrices.

Is W = {A in Mnxn : A^x = A} a subspace of V?


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  • Linear Algebra - ,

    No, because if A is in W, then

    B = lambda A

    is not in W if lambda is not equal to 1:

    A^x = A --->

    B^x = lambda^x A^x = lambda^x A =

    labda^(x-1) B

    which is not equal to B for general lambda.

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