Similar Linear Operators with Different Bases | Linear Algebra

We discuss matrices for linear operators with respect to different bases. We'll study the relationship that exists between transformation matrices for the same linear operator, prove a theorem establishing an equivalence between identity operators and transition matrices, and a theorem connecting linear operators with respect to different bases. We finish by discussing similarity invariants, and the determinant and eigenvalues of a linear operator. #linearalgebra

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0:00 Intro
1:20 A Simple Transformation Matrix
4:53 Transition Matrices
7:12 Transition Matrices and Identity Operators
10:20 Connecting Transformation Matrices with Different Bases
16:22 Example of Similar Operators
18:47 Similarity Invariants
20:33 Determinant of a Linear Operator
21:30 Eigenvalues of a Linear Operator
23:02 Conclusion

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Outro music by Ben Watts and is available for channel members.

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