Linear Algebra

5.

Linear Transformations

5.1.

Introduction to Linear Transformations

5.1.1.

Definition and linearity conditions

5.1.2.

Domain and codomain

5.1.3.

Linear transformations from Rⁿ to Rᵐ

5.1.4.

Geometric transformations in R²

5.1.4.1.

5.1.4.2.

5.1.4.3.

5.1.4.4.

Scaling transformations

5.1.4.5.

Shear transformations

5.1.5.

Composition of transformations

5.1.6.

Identity and inverse transformations

5.2.

Kernel and Image

5.2.1.

Kernel of a linear transformation

5.2.2.

Image of a linear transformation

5.2.3.

Computing kernel and image

5.2.4.

Rank and nullity of transformations

5.2.5.

Fundamental theorem of linear transformations

5.3.

Matrix Representation

5.3.1.

Standard matrix of a linear transformation

5.3.2.

Finding matrix representations

5.3.3.

Matrix-vector multiplication as transformation

5.3.4.

Change of basis for transformations

5.3.5.

Matrix similarity

5.4.

Special Types of Linear Transformations

5.4.1.

One-to-one transformations

5.4.2.

Onto transformations

5.4.3.

5.4.4.

Invertible transformations

5.4.5.

Isomorphic vector spaces

Previous

4. Vector Spaces and Subspaces

Go to top

Next

6. Inner Products and Orthogonality