Linear map

For vector spaces \(V\) and \(W\) over field \(K\), \(f: V \rightarrow W\) is a linear map if \(\forall \mathbf u, \mathbf v\in V, \forall c \in K\) holds:

• Additivity: \(f(\mathbf u+ \mathbf v) = f(\mathbf u) + f(\mathbf v)\)
• Homogeneity: \(f(c \mathbf u) = c f(\mathbf u)\)