CS223 · Chapter 5 · Annotated SlidesEigenvectors and Linear Transformations
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Eigenvectors and Linear Transformations

The matrix of a linear transformation relative to bases, the B-matrix [T]_B = P⁻¹AP, and diagonal matrix representations.

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  4. 4 In the previous examples, the transformation was given as A description, but the standard matrix was NOT given . M Therefore, the way to find the matrix (the B-Matrix – the T matrix of relative to basis) is by applying the following
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In the previous examples, the transformation was given as A description, but the standard matrix was NOT given . M Therefore, the way to find the matrix (the B-Matrix – the T matrix of relative to basis) is by applying the following

Slide 4: In the previous examples, the transformation was given as A description, but the standard matrix was NOT given . M Therefore, the way to find the matrix (the B-Matrix – the T matrix of relative to basis) is by applying the following

Notes

  1. The B-matrix of x ↦ Ax is [T]_B = P⁻¹AP where P has the basis vectors as columns. If B is an eigenvector basis, [T]_B is diagonal.

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