In this talk we shall see how the notion of diagonalization of a self-adoint matrix can be used to obtain analogous representation for every matrix A, namely, the singular value decomposition (SVD), and how the SVD is helpful in representing the Moore-Penrose inverse of a matrix, and thereby, obtaining a representation for the generalized solution, the least-square solution of minimal norm, for the matrix equation Ax=b. We shall also discuss the SVD in the infinite dimensional setting, and see how it is useful in inferring the effect of data errors on the generalized solution of a compact operator equation.
Prof. M. Thamban Nair is a distinguished mathematician currently serving as a Visiting Professor at BITS Pilani, Goa Campus. Previously, he was a Professor and Head of the Department of Mathematics at IIT Madras. He earned his M.Sc. in Mathematics from the University of Calicut and his Ph.D. in Mathematics from IIT Bombay.
His research broadly focuses on Applicable Functional Analysis, with special emphasis on spectral approximation, operator equations, and inverse & ill-posed problems. He has authored several books and is the recipient of multiple awards recognizing his contributions in\r\nmathematics research and teaching.
