Signature matrices: The eigenvalue problem
Dealing with matrices can give us a hard time, especially when their dimension is too big, but we also well know how valuable information a matrix may carry, and that is why we study them. When a matrix has a significant number of zeroes we realize how much easier all calculations are. For instance, the product will be simpler to calculate, the determinant, the inverse and even the eigenvalue problem. ^ This thesis provides the description and behavior of a very special kind of matrices which we call signature matrices, definition that is due to Piotr Wojciechowski. A particular feature of these matrices lies in the fact that most of their elements are zeroes which makes significantly easier to work with them. The motivation that led us to analyze these matrices is that they play an important role in the study of partially-ordered algebras with the Multiplicative Decomposition Property. This topic will be brie y described in the Preliminaries chapter, while the formal definition and the properties of the signature matrices constitute the main part of this thesis. We will also give some possible applications and state some questions that still have no answers but seem to be very trackable. ^
Aguirre Holguin, Valeria, "Signature matrices: The eigenvalue problem" (2010). ETD Collection for University of Texas, El Paso. AAI1477761.