"Linear Algebra and its Applications"-chaper6-orthogonality and least squares-least squares problem

Least squares problem:

Before the combination of orthogonal, subspace W, orthogonal projection, orthogonal decomposition theorem and best approximation principle in vector space, the least squares problem can be solved satisfactorily.

First of all, we have to explain the problem itself, that is, in the process of production, for the giant linear systems ax=b, may be no solution, but we are urgently need a solution, satisfies the solution is the most approximate solution of the equation.

Below we synthesize a series of concepts, theorems, to solve this problem.

First we need to give the definition of the most approximate solution:

We need to stand in a new angle to understand the ax=b of linear equations, which can help us solve the problem better.

The most generalized solution to the least squares problem is given above, but considering the specific calculation seems to be a bit of a hassle, let's explore an algorithm based on the above principle.

"Linear Algebra and its Applications"-chaper6-orthogonality and least squares-least squares problem