Introduction

Null Spaces

The null space of a matrix A are all vectors so that .

Bases

A basis to a space is a chosen set of vectors so that any vector in the space can be uniquely expressed in terms of the basis vectors:

Example: are a basis to coordinate space:

Basis vectors are independent, i.e.

only when all coefficients are zero. So you cannot express one basis vector in terms of the rest.

Rank

The rank of a matrix is the number of independent rows or columns.

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