Linear Algebra - Module 2

Derivation of Singular value Decomposition (SVD) and pseudoinverse

The note is about Derivation of Singular Value Decomposition first by assuming Columns of A are independent which in turn leads to economical form of SVD. It is followed by generic case. Finally it is shown how it is used for solving linear regression problem which is basically a leastsquare , least_norm solution for x, the regression coefficients. Regression involves a projection (leastsquare error part) and a leastnorm solution part which insist that the solution vector x must be in rowspace of the associated data matrix A.