Diagonalizing Matrices and Diagonalizability | Linear Algebra

We go over diagonalizing matrices and how to determine diagonalizability. We'll see several important theorems (and a proof) concerned with the diagonalizability of a matrix as well as see several examples, including showing a matrix is not diagonalizable. #linearalgebra

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0:00 Intro
0:15 Definition of Diagonalizable Matrix
1:03 An nxn Matrix is Diagonalizable if and only if it has n Linearly Independent Eigenvectors
1:33 Proof: Forward Direction
5:45 Proof: Reverse Direction
9:01 Distinct Eigenvalues have Linearly Independent Eigenvectors
10:05 Steps to Diagonalize a Matrix
11:23 Diagonalizing a 3x3 Matrix
15:54 Showing a Matrix isn't Diagonalizable
17:08 Check if a Matrix is Diagonalizable
18:15 Diagonalizable at a Glance
19:01 Conclusion

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