Given a real N by N matrix A, write p(A) for the maximum angle by which A rotates any unit vector. Suppose that A and B are positive definite symmetric (PDS) N by N matrices. Then their Jordan product {A, B} := AB + BA is also symmetric, but not necessarily positive definite. If p(A) + p(B) is obtuse, then there exists a special orthogonal matrix S such that {A, SBS^(-1)} is indefinite. Of course, if A and B commute, then {A, B} is positive definite. Our work grows from the following question: if A and B are commuting positive ...
continued below

With locations on the Denton campus of the University of North Texas and one in Dallas, UNT Libraries serves the school and the community by providing access to physical and online collections; The Portal to Texas History and UNT Digital Libraries; academic research, and much, much more.

Given a real N by N matrix A, write p(A) for the maximum angle by which A rotates any unit vector. Suppose that A and B are positive definite symmetric (PDS) N by N matrices. Then their Jordan product {A, B} := AB + BA is also symmetric, but not necessarily positive definite. If p(A) + p(B) is obtuse, then there exists a special orthogonal matrix S such that {A, SBS^(-1)} is indefinite. Of course, if A and B commute, then {A, B} is positive definite. Our work grows from the following question: if A and B are commuting positive definite symmetric matrices such that p(A) + p(B) is obtuse, what is the minimal p(S) such that {A, SBS^(-1)} indefinite? In this dissertation we will describe the level curves of the angle function mapping a unit vector x to the angle between x and Ax for a 3 by 3 PDS matrix A, and discuss their interaction with those of a second such matrix.

This dissertation is part of the following collection of related materials.

UNT Theses and Dissertations

Theses and dissertations represent a wealth of scholarly and artistic content created by masters and doctoral students in the degree-seeking process. Some ETDs in this collection are restricted to use by the UNT community.

Bajracharya, Neeraj.Level Curves of the Angle Function of a Positive Definite Symmetric Matrix,
dissertation,
December 2009;
Denton, Texas.
(digital.library.unt.edu/ark:/67531/metadc28376/:
accessed November 17, 2017),
University of North Texas Libraries, Digital Library, digital.library.unt.edu;
.