Pseudoinverse

$$A^+ = (A^T A)^{-1} A^T$$

Here, $A$ is a matrix with linearly independent columns and $A^+$ is its pseudoinverse. If $A$ is of size $m \times n$, $A^+$ is of size $n \times m$.

The idea is that if $A$ does not have an inverse, the pseudoinverse is the closest approximation. See also the least squares solution.