A mapping between two vector spaces that preserves the underlying structure of those spaces.
A linear map (or linear transformation) is a function between two vector spaces that preserves vector addition and scalar multiplication, and .
T - The name of the transformation or map.
V - The domain, which is the vector space of all possible inputs.
-> - The mapping symbol, indicating the direction of the action from input to output.
W - The codomain, which is the vector space where all outputs land.
- Matrix Representation: In finite dimensions, every linear map can be represented as a matrix. Applying the map to a vector is equivalent to multiplying the matrix by that vector.