Least Squares Solutions

This lecture introduces the concept of least squares solutions, where a matrix A of size mxn is used to find the solution to the equation Ax=b. The distance between the actual and approximated values is defined as the error of approximation. The lecture covers the normal system associated with the least squares solutions, the uniqueness of orthogonal decomposition, and the determination of solutions using matrix operations. Examples are provided to illustrate the application of least squares solutions in finding solutions to linear systems. The lecture concludes with the theorem of best approximation and the method of least squares, emphasizing the importance of linear independence and the properties of the matrix ATA.