Worked example

a: 1	2
2	4

→ rank(A) = 1

Method and scope

Rank counts independent pivot columns after row scaling and elimination. Zero matrices have rank zero. Tolerance is ε×32×max(rows,columns) on scaled rows; numerical rank near dependence can change with rounding.

0 ≤ rank(A) ≤ min(m,n)

Precision and limits

≈ marks an approximation. Display rounding does not change the internal calculation.

Sources