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Introduction to Linear Maps (Linear Transformations)

Handwritten introduction to linear maps showing the notation T: V → W and the two properties of linearity: vector addition and scalar multiplication.

Linear Maps

Handwritten introduction to linear maps and linear transformations, page 1 of 4.
Handwritten introduction to linear maps and linear transformations, page 2 of 4.
Handwritten introduction to linear maps and linear transformations, page 3 of 4.

Properties of a Linear Map

Handwritten explanation of the properties of a linear map, page 1 of 2: addition and scalar multiplication.
Handwritten explanation of the properties of a linear map, page 2 of 2: addition and scalar multiplication.

Example 1

Worked linear transformation example in handwritten notes, page 1 of 3.
Worked linear transformation example in handwritten notes, page 2 of 3.
Worked linear transformation example in handwritten notes, page 3 of 3.

Example 2

Second worked linear transformation example in handwritten notes, page 1 of 5.
Second worked linear transformation example in handwritten notes, page 2 of 5.
Second worked linear transformation example in handwritten notes, page 3 of 5.
Second worked linear transformation example in handwritten notes, page 4 of 5.
Second worked linear transformation example in handwritten notes, page 5 of 5.

Recognizing Linear Maps (Or When it is Nonlinear)

e.g.

Handwritten notes on recognizing linear and nonlinear maps, page 3 of 4.
Handwritten notes on recognizing linear and nonlinear maps, page 4 of 4.

Matrices and Linear Maps

Handwritten notes explaining matrix representations of linear maps, page 1 of 2.

e.g.

Handwritten notes explaining matrix representations of linear maps, page 2 of 2.

Proving Linearity Using Matrix Representation

Handwritten proof notes on linear maps and matrix representations, page 1 of 7.

Proof

Handwritten proof notes on linear maps and matrix representations, page 2 of 7.
Handwritten proof notes on linear maps and matrix representations, page 3 of 7.
Handwritten proof notes on linear maps and matrix representations, page 4 of 7.
Handwritten proof notes on linear maps and matrix representations, page 5 of 7.
Handwritten proof notes on linear maps and matrix representations, page 6 of 7.

e.g.

Handwritten proof notes on linear maps and matrix representations, page 7 of 7.
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