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Linear Algebra: Lecture 30: eigenspace decompositions, orthonormality

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Published on Apr 6, 2015

First 22 minutes or so: Here we conclude our study of LI of eigenvectors. We find that eigenspaces form a direct sum, however, as we saw in previous lectures, the sum may not cover the entire Rn. When the sum of the eigenspaces covers all of Rn then we have a matrix which is diagonalizable. Then the remaining time is devoted to the study of geometry in Rn, in particular the concept of the "perp" aka the orthogonal complement is unveiled. There is more to say in future lectures.

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