Linear Algebra

Vector Space

Definition

Motivation: properties of addition and scalar multiplication in $ \mathbf{F}^n $

flowchart LR
	subgraph addGroup["$$u + v$$"]
		direction TB
		addSet["&bull; commutativity<br/>&bull; associativity<br/>&bull; 0<br/>&bull; -v"]
	end
	subgraph scalarGroup["$$\lambda v$$"]
		direction TB
		scalarSet["&bull; associativity<br/>&bull; 1"]
	end
	addSet <-->|distributive<br/>properties| scalarSet
	style addGroup fill:transparent,stroke:transparent
	style scalarGroup fill:transparent,stroke:transparent

Examples

• $ \mathbf{F}^S $
• $ \mathcal{P}(\mathbf{F}) $
• $ \mathcal{P}_m(\mathbf{F}) $
• $ \mathcal{L}(V, W)$