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Vector Space

Set of Objects, called vectors , in which two operations are defined. called addition and scalar multiplication

Subspace

A subset H of some Vector Space V such that H has these properties.

Null Space

the set of all solutions to the homogenous equation Ax=0

Column Space

The set of all linear combinations of the columns of A

Basis

A set of linearly independent vectors which spans the space.

Row Space

the set of all linear combinations of the vectors formed from the rows of A also noted as the ColAT

Rank

the dimension fo the cloumn space of A