Linear Mappings
A very special class of functions between vector spaces.
Algebraic Definition
Injectivity, Surjectivity
Matrix Representation
Change of Basis
Rank-Nullity
In this section, we associate a linear transformation $T: V \rightarrow W$ with 2 extremely useful subspaces we call the image and kernel of $T$
- Lets us safely interpret a linear transformation as annihilating its kernel and sending the span of the remaining basis vectors onto the image
Kernel/Null Space
Image/Column Space
Dimension Theorem
Rank
Other Fundamental Subspaces
