Determining Transformation
[L2 Norm](https://texonom.com/l2-norm-38c15917350a4c82a11003474ac7d280) 


### $x'$ is measured location and $M$ is unknown matrix
$$x' = Mx$$
### Least Square Error Function $f(x_i; p)$ is predicted location

$$E_{LS} = \Sigma_i||f(x_i;p) - x'_i||^2 $$
### $p$ is parameter
$$\hat{p} = argmin_p E_{LS}$$

### Determining Transformation Notion
|Title|
|:-:|


### General form of linear least squares in matrix form
$$E_{LS} = ||Ax - b||^2$$
$$= x^T(A^TA)x - 2x^T(A^Tb) + ||b||^2$$
### When you solve derivative
$$(A^TA)x = A^Tb$$
$$x = (A^TA)^{-1}A^Tb$$
but inverse of Matrix sucks








