Speaker

:

Prof. A.R. Shastri

Affiliation

:

IIT, Mumbai (Graduate Seminar)
 

Subject Area

:

Mathematics

Venue

:

Lecture Hall - II (Ground floor), Dept of Mathematics

Time

:

4.00 pm

Date  

:

Tuesday,  23rd May, 2006

Event Title1

:

GAUSS ELIMINATION METHOD AND LAGRANGE-BELTRAMI FORMULA

 Let $Q(x_1,\ldots, x_n)$ be a symemtric (hermitian), positive definite, bilinear form in $n$-variables. A classical Lagrange-Beltrami formula obtained as an easy corollary of spectral theorem says that after a change of basis, $Q$ can be expressed as a `sum of squares' $$(y_1,\ldots, y_n) = \sum_{i=1}^n \delta_i y_i^2.$$It is well know that the coefficients $\delta_i$ can be expressed in terms of the leading principal minors of the original symmetric matrix repesenting the form $Q.$ In this talk, using one single tool viz. Gauss Elimination Method,we shall give a simple proof of the above result as well as explicit formula for the change of basis that should be carried out.Related problems about indefinite forms etc. will be also discussed. The talk is accessible to all Math students.