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Auburn University’s College of Sciences and Mathematics Colloquia are held on Fridays in Parker Hall, Room 250, from 4:00-4:50 (unless otherwise advised).

Refreshments are served in Parker Hall, Room 244, beginning at 3:30.

March 23, 2012

Speaker: Fuzhen Zhang (Nova Southeastern University, Fort Lauderdale, FL)

Title: The Schur Complement

Abstract: Auburn is the birthplace of the mathematical term “Schur complement.” This talk will present the historical connection of Auburn and the term, review classical results, and show some new results on the topic.

Faculty host: T. Y. Tam

A brief bio: Fuzhen Zhang has about 50 research articles. He authored two books (Linear Algebra: Challenging Problems for Students, Johns Hopkins University Press, 1996; 2nd edition 2009. Matrix Theory: Basic Results and Techniques, Springer, 1999; 2nd edition 2011) and edited the book The Schur Complement and Its Applications, Springer 2005). He is an associate editor of several journals, including Linear and Multilinear Algebra, International Journal of Information and Systems Sciences, Banach Journal of Mathematical Analysis (BJMA). He is also a collaborating editor for the American Mathematical Monthly.

Dr. Emilie Haynsworth was the first to call it the Schur complement. She directed the work of 18 students who earned doctorates, all at Auburn University.

Do you know these matrices described by Alan Rendall? If so, please point out a source where he may find more information about them. I am interested in knowing too!

I have come across a class of matrices with some interesting properties. I feel that they must be known but I have not been able to find anything written about them. This is probably just because I do not know the right place to look. I will describe these matrices here and I hope that somebody will be able to point out a source where I can find more information about them. Consider an $latex n\times n$ matrix $latex A$ with elements $latex a_{ij}$ having the following properties. The elements with $latex i=j$ (call them $latex b_i$) are negative. The elements with $latex j=i+1\ {\rm mod}\ n$ (call them $latex c_i$) are positive. All other elements are zero. The determinant of a matrix of this type is $latex \prod_i b_i+(-1)^{n+1}\prod_i c_i$. Notice that the two terms in this sum always have opposite signs. A property of these matrices which I…

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Had to reblog this post! I love linear algebra and programming. I am very interested in learning more about REDUCE and REDLOG.