Is this Linear Transformation Isomorphic? Given that a Matrix is Nilpotent

Asked Oct 23 '17 at 05:01

Active Oct 23 '17 at 07:36

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Given a matrix in $M_{n \times n}$ which is nilpotent. Prove that the Linear Transformation $T:M_{n \times n} \rightarrow M_{n \times n}$ given by $T(X) = X -NX$ is an isomorphism.

Shouldn't be answered with Eigenvalues and Eigenvector, it should only be answered using matrices, vector spaces, Linear transformations.

edited Oct 23 '17 at 07:36

Douglas Molin

1,281

asked Oct 23 '17 at 05:01

diegocuehdz

I saw that earlier, the issue is that the problem shouldn't be answered with Eigenvalues and Eigenvector, it should only be answered using matrices, vector spaces, Linear transformations. Any Ideas? – diegocuehdz Oct 23 '17 at 05:11
@Musicue If that is the case then you should edit the question to reflect that. – Sriotchilism O'Zaic Oct 23 '17 at 05:14
Done, sorry I'm new to this. Thanks for the advice. – diegocuehdz Oct 23 '17 at 05:16

Is this Linear Transformation Isomorphic? Given that a Matrix is Nilpotent

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