**Date & Time:** Friday, October 23, 2008, 16:00- 17:00.

**Venue:** Ramanujan Hall

**Title:** Interplay of Ranks of Submatrices

**Speaker:** Ravindra B. Bapat, Indian Statistical Institute, New Delhi

**Abstract:** We first discuss some results for rank, some of which are not so well-known. Then we present different proofs of the "nullity theorem" which asserts that any submatrix of a nonsingular matrix *A*, and the complementary submatrix in the inverse of *A*, have the same nullity. Applications of the nullity theorem to structured matrices, including tridiagonal and banded matrices, are described.

The talk will be accessible to both MSc and PhD students.