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Linear Algebra: Lecture 28: adjoint formula for inverse, eigenvectors and values

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Published on Mar 31, 2015

I give another 14 minutes or so on determinants application to equations of lines and planes and the classical formula for the inverse in terms of the adjoint. Please read Proof II for the inverse formula as I didn't find time to go through it this time. Then, the last part of class introduces e-vectors and e-values. We prove the characteristic equation gives all the possible e-values for a given matrix A and hence a transformation T on a finite dimensional vector space. Finally, we conclude with a proof that the existence of an eigenbasis (a basis of e-vectors for A) implies A is similar to a diagonal matrix where the diagonal values are the e-values of A.

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