LINEAR ALGEBRA SEMINAR
Tuesday 4:00-5:00 p.m. Parker 224
NO SEMINAR UNTIL SPRING SEMESTER
HAPPY HOLIDAYS
GOOD LUCK ON FINALS
Speaker: Prof. Thomas H. Pate
Title: Immanants Orderings and Inequalities Involving Generalized Matrix Functions
Abstract: I will discuss the partial ordering induced upon the set of irreducible characters of the symmetric groups via the set of Hermitian positive semi-definite matrices.
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November 6, 2012
Speaker: Avantha Indika
Title: Orthogonal bases of Brauer symmetry classes of tensors for the dihedral group.
Abstract: We will give the necessary and sufficient conditions for the existance of an orthogonal basis consisting of standard decomposable tensors of a symmetry class of tensors associated with a Brauer character of the dihedral group.
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October 30, 2012
Speaker: Tin-Yau Tam
Title: Marcus-Oliveira Conjecture on the Determinants of the Orbit Sum
Abstract: We will review Fiedler's result on the determinant of sum of two Hermitian matrices. Then we discuss analogous results of Tin-Yau Tam and Mary Clair Thompson. Marcus-Oliveira conjecture will be introduced. If you Google by the key words: Marcus Oliveira conjecture, you will get a lot of information on the web.
For full presentation pdf, click here
October 23, 2012
Speaker: Peter Nylen
Title: Realizations of Interlacing by Structured Matrices
Abstract available here
October 16, 2012 NO SEMINAR
October 9, 2012
Speaker: Daniel Brice
Title: Derivations of Parabolic Subalgebras II
Abstract: Consider p, a parabolic subalgebra of a complex semisimple Lie algebra g. We will show that every derivation of p is of the form ad z for some z in p. If time permits, we will also prove the real case.
October 2, 2012
Speaker: Douglas Leonard
Title: Thinking outside the matrix
Abstract available here
September 25, 2012
Speaker: Daniel Brice
Title: Der(g) where g is parabolic
Abstract: Let g be a parabolic subalgebra of a finite-dimensional reductive Lie algebra L over the real or complex field. The derivation algebra Der(g) consists of linear endomorphisms f of g that satisfy f([x,y])=[f(x),y]+[x,f(y)] for all x, y in g. The speakers examine the structure of Der(g), especially as it relates to the grading on g given by the root space decomposition of L. The speakers will give a short survey of existing related literature as well as present some new results. The presentation will be accessible to a general audience familiar with basic linear algebra techniques.
For full presentation PDF, click here
September 18, 2012
Speaker: Dr. Wen Yan (Tuskegee University)
Title: Anti-Diagonals of Symmetric and Skew-symmetric Matrices with Prescribed Eigenvalues
Abstract: The complete relationship between the k-th anti-diagonals and the eigenvalues of an n-by-n real symmetric matrix is obtained. When k is even, the relationship is weak majorization. The Hermitian case is also studied. Similar results are obtained for real and complex skew symmetric matrices.
For full presentation PDF, click here
September 11, 2012
Speaker: Wen Yan (Tuskegee University)
Title: Anti-Diagonals of Symmetric and Skew-symmetric Matrices with Prescribed Eigenvalues
Abstract: The complete relationship between the k-th anti-diagonals and the eigenvalues of an n-by-n real symmetric matrix is obtained. When k is even, the relationship is weak majorization. The Hermitian case is also studied. Similar results are obtained for real and complex skew symmetric matrices.
September 4, 2012
Speaker: Mary Clair Thompson
Title: The Gelfand-Naimark Decomposition
Abstract: We decompose the Lie group G with the Gelfand-Naimark Decomposition, and iterate the process to create a sequence. We investigate the convergence of the sequence for certain elements of G.
August 28, 2012
Speaker: Mary Clair Thompson (advisor: Tin-Yau Tam).
Title: The Convergence of the Iterated Aluthge Transform