Linear Algebra 19m: Matrix Representation of a LT - Vectors in ℝⁿ, Eigenbasis

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Excellent video. As for the question at the end, in general the answer should be know. Since the eigenvalues are the same, so the trace and determinant should also be the same. The trace is not necessarily the trace of the identity and the determinant is not necessarily 1.

adarshkishore
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i can not give enough likes for these videos. are group theory and linear algebra & tensor analysis sort of different branches or they meet at some point?

sandip
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So in response to your question at the end, I'm pretty sure that if we had chosen our basis such that the basis vectors were the eigenvectors of the linear transformation each divided by its corresponding eigenvalue, we should get the identity matrix, assuming a non-defective linear transformation?

And with a defective linear transformation perhaps we supplement (in the basis) the 'specific' eigenvectors with a number of generalized eigenvectors equal to the defect and then divide those by their respective (repeated) eigenvalues?

knivesoutcatchdamouse