Least Squares Formula PROOF

The video provides a detailed explanation of the least squares method using linear algebra. It begins by revisiting the ordinary least squares method and introduces a new approach to solve for the best fit curve by minimizing the error term. The concept of column space is explained, and the orthogonality condition is used to derive matrix equations. The video demonstrates how to solve for the optimal parameters using matrix inversion and discusses practical considerations like using the pseudo-inverse in Matlab for robust calculations.

What is the purpose of the ordinary least squares method?

Explain how the vector X is related to the least squares method.

What does it mean to minimize the norm of AX minus B squared?

Describe the significance of the column space in the context of the least squares method.

What happens if the vector B does not lie on the plane defined by the column space?

How can the best value of AX be determined when B is not on the plane?

What is the relationship between the vectors A1, A2, and the orthogonality condition in the least squares method?