Algebra Seminar: The Numerical Range of a matrix and Non-Negative Matrices
1:00p.m. Neill 106W
Abstract: In this presentation we will survey the numerical range of a matrix by stating and proving some basic properties that it possesses and by mentioning some important open problems. In the second portion of the presentation, we will digress from the aforementioned topic and briefly discuss non-negative matrices. In particular, we will discuss basic properties of non-negative matrices and the Perron-Frobenius Theorem for non-negative matrices. Finally, we will examine the numerical range of a non-negative matrix and consider one of the previously mentioned open problems; i.e. whether or not zero lies in the numerical range (either in the interior or the boundary).