Linearity

Linearity refer to set of two properties:

• Additivity, and
• Homogeneity of degree one.

Examples

Linear transformation

\(V\) and \(W\) are vector spaces over field \(F\), a linear transformation \(L: V \to W\) satisfies:

Additivity

\(L(\mathbf{u} + \mathbf{v}) = L(\mathbf{u}) + L(\mathbf{v})\), where \(\mathbf{u}, \mathbf{v} \in V\).

Homogeneity of degree one

\(L(c\mathbf{v}) = cL(\mathbf{v})\), where \(c \in F\).

References

1. Linearity
2. Function Space
3. Homomorphism