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Changing bases for a linear transformation
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Generalized Dilations and Eigenvalues - Wild Linear Algebra A - NJ Wildberger
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- 1 CONTENT SUMMARY: pg 1: @ introducing the 2nd most important problem in linear algebra; 2 frames of reference; desire to compare frames of reference; example using "Bob" and "Rachel" basis vectors;
- 2 pg 2: @ example of vector change of basis; going back and forth between "Bob's" and "Rachel's" systems;
- 3 pg 3: @ notation to facilitate change of basis conversation; ordered bases, coordinate vectors, change of basis matrix; change of basis matrices are inverse matrices;
- 4 pg 4: @ process to obtain change of basis matrix; examples to verify agreement to earlier results;
- 5 pg 5: @ how linear transformations appear when going from one frame of reference to another frame of reference; start with an example;
- 6 pg 6: @ example continue; the same linear transformation expressed in different frames of reference; the transformation is much more easily expressed in "Rachel's" system;
- 7 pg 7: @ Definition of similar matrices; Similar matrices represent the same linear transformation but with respect to w.r.t. different bases
- 8 Introduction
- 9 Between Bob and Rachels systems
- 10 Ordered bases and coordinate vectors
- 11 Changing bases for a linear transformation
- 12 Similar matrices
- 13 Generalized dilations
