Vector Spaces

R^{n}

and

C^{n}

-Complex Numbers-Addition and multiplicationProperties

- α,

subtraction,

1 / α,

divisionLists-List, lengthDifferent list and set

F^{n}

-Addition in

F^{n}

Commutativity of addition in

F^{n}

Definition

0

Additive inverse in

F^{n}

Scalar multiplication in

F^{n}

Subspaces-Conditions for a subspaceSums of Subspaces-Sum of subspaces is the smallest containing subspaceDirect Sums-Condition for a direct sumDirect sum of two subspacesDefinition of Vector Space-Definition vector, pointNotation

F^{S}

Unique additive identityUnique additive inverseThe number

0

times a vectorA number times the vector

0

The number

- 1

times a vector