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Chapter Three: Maps Between Spaces

Isomorphisms

Homomorphisms

ComputingLinearMaps

MatrixOperations

ChangeOfBasis

Projection

Topics

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The prior section shows how matrices represent linear maps. A good strategy, on seeing a new idea, is to explore how it interacts with some already-established ideas. In the first subsection we will ask how the representation of the sum of two maps f+g is related to the representations of the two maps, and how the representation of a scalar product r\cdot h of a map is related to the representation of that map. In later subsections we will see how to represent map composition and map inverse.

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