Acts as a central hub for understanding transformations between vector spaces, covering domains, codomains, images, and kernels # 🧭 Index - [[Composition of Linear Mappings]] - The process of applying one linear mapping after another - [[Domain & Codomain]] - Domain is the set of inputs, codomain is the set of outputs - [[Image]] - The set of all possible outputs of a linear map - [[Kernel]] - The set of all vectors in the domain that map to the zero vector under a transformation - [[Linear Mapping (Transformations)]] - A function $T: V \to W$ between vector spaces that preserves vector addition and scalar multiplication - [[Matrix Mapping (Transformations)]] - The operation of applying a matrix to a vector, which computes a new vector as a linear combination of the matrix’s columns. - [[Matrix-Vector Multiplication]] - The operation of applying a matrix to a vector, which computes a new vector as a linear combination of the matrix’s columns - [[Range]] - The actual set of outputs produced by a linear transformation for all inputs in the domain.