Solve where has size .
Because we use the 2-norm, the solution is found when (Pythagorean theorem).
This is equivalent to the equation
See dot product and orthogonality.
This equation is a linear equation in with a square matrix .
Nov 19, 20241 min read
Solve x∗=argminx∥Ax−b∥2 where A has size m×n.
Because we use the 2-norm, the solution is found when Ax−b⊥span(A) (Pythagorean theorem).
This is equivalent to the equation
AT(Ax−b)=0(ATA)x=ATbSee dot product and orthogonality.
This equation is a linear equation in x with a square matrix ATA.