# Dimension

### From Glossary

- Of a set: the dimension of the smallest affine space that contains the set. The dimension of an affine space is if the maximum number of
affinely independent points in the set is . Of particular interest is the
*column space*of a matrix ,. The dimension of this is the rank of . Another is the*row space*of ,. The dimension of this is also the rank of . - Of an expression: the units of measurement (e.g., tons of apples,
meters of rope, hours of labor). In a relation,
such as , the units of , and must all be the same.
*Dimensional analysis*is concerned with determining such consistency and inferring whatever units are missing.