Statistics and Data Science Seminar
Bhaskara Rao Kopparty
Indiana State University
Generalized Inverses Of Matrices: Not Just For Real Or Complex Matrices
Abstract: Yes. That is true. All of us know that some real and complex matrices have inverses. Not all of them. But we also know that all real and complex matrices have generalized inverses. These are extensively used by statisticians. What about matrices that have only integer entries? Would such a matrix have a generalized inverse whose entries are all integers? What if a matrix has all entries as polynomials? We shall discuss various questions about generalized inverses and see some exciting results.
Here is one of the results: An integer matrix of rank r has a generalized inverse if and only if the greatest common divisor of all r x r minors of A is 1.
Wednesday April 4, 2012 at 4:00 PM in SEO 636