normal equation and non-invertibility(cs229)

redundant features ($x^{(i)}$s are linearly dependent)

• for example, $x_1$ is size in feet square, meanwhile, $x_2$ is size in meter square. For all data, $x_1 = (3.28)^2x_2$ will lead to a non-invertible $(mathbf{X^top}mathbf{X})^{-1}$

Too many features, i.e. $mlt n$

• We have $m$ conditions(data) but if there were $n$ unknowns and $n$ is greater than $m$, the solution can not be solve.
• To solve the problem, delete some features, or use regularization.