Class 1
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Preliminaries
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Handouts:
- Miscellaneous:
- typo in text:
on page 528, in the definition of a complex inner product space: condition (a) should read "(u,u) ge 0" and not "(u,v) ge 0".
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Linear Transformations and Matrices, Chapter 4,
Sections 4.1 (Pages 253-)
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fundamental equation of linear algebra:
f(ax + by) = af(x) + bf(y), for all scalars a,b, and for all vectors x,y
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definition of linear transformation (and linear operator)
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simplest examples of linear transformations
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further examples and geometry of linear (and nonlinear) transformations
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verification of a linear transformation (proofs using the definition)