A m × n system of linear equations with m < n is overdetermined.
There are more equations than there are unknowns. ”Solving” this equation is the process
of reducing the system to an m × m problem then solving the reduced set of
equations. A common technique for constructing a reduced set of equations is known as the
least squares solution to the equations. The least squares equations are derived by
premultiplying Equation
35 by A^{T}, i.e.

$\mathbf{\left({A}^{T}A\right)x={A}^{T}b}$ | (42) |

Often Equation 42 is referred to as the normal equations of the linear least squares problem. The least squares terminology refers to the fact that the solution to Equation 42 minimizes the sum of the squares of the differences between the left and right sides of Equation 35.