Department of Mathematics

Indian Institute Of Technology Madras , Chennai
  • Department of Mathematics-Shifted to NAC Office of the Department of Mathematics is moved from HSB to New Academic Complex (NAC) 5th and 6th Floor

Generalized Inverses of Matrices by Inversion of Complemented Matrix and its Application to Generalized Linear Model

Speaker : Prof. Eagambaram Narayanan (Former Deputy Director General, Indian Statistical Service, Government of India)

11-10-2018

Abstract :

A solution $X$ to to the matrix equation $'AXA = A'$ is known as a generalized inverse (g-inverse) of $A$ and a solution $X$ to $'XAX = X'$ is called an outer-inverse of $A$. Given a square matrix $A$, we can choose $C$ disjoint with $A$ such that $A+C$ is nonsingular. The inverse of $A+C$ produces all g-inverses of $A$. By this Inverse Complemented Matrix (ICM) method we can characterize all g-inverses and outer-inverses of $A$. The ICM provides a better approach to study the Generalized Linear Model (GLM), $Y = X\beta + \epsilon, var (\epsilon) = \sigma^{2}V$, by decomposing the design matrix $X$ and variance matrix $V$ appropriately.

Key Speaker Prof. Eagambaram Narayanan (Former Deputy Director General, Indian Statistical Service, Government of India)
Place NAC 522
Start Time 3:00 PM
Finish Time 4:00 PM
External Link None