User:IssaRice/Linear algebra/Rank

$T:V\to W$

$A$ is m by n matrix

• $\dim \mathrm{r}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e}T$
• dimension of row space of $A$
• dimension of column space of $A$
• number of non-zero rows in the echelon form matrix of $A$
• number of pivots in the echelon form matrix of $A$
• number of linearly independent rows in $A$
• number of linearly independent columns in $A$