Linear Transformations

Definition and linearity conditions

Domain and codomain

Linear transformations from Rⁿ to Rᵐ

Geometric transformations in R²

Composition of transformations

Identity and inverse transformations

Kernel of a linear transformation

Image of a linear transformation

Computing kernel and image

Rank and nullity of transformations

Fundamental theorem of linear transformations

Standard matrix of a linear transformation

Finding matrix representations

Matrix-vector multiplication as transformation

Change of basis for transformations

Matrix similarity

One-to-one transformations

Onto transformations

Isomorphisms

Invertible transformations

Isomorphic vector spaces