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| Positive Definite Matrices | Positive Semi-Definite(PSD) Matrices | |
| Eudclidan Distance Matrices |
||
| Completely Positive (CP) Matrices | Doubly Nonnegative (DN) Matrices | |
| Strictly
Copositive |
Copositve |
|
| M-Matrices | M0-Matrices | |
| Symmetric M-matrices | Symmetric M0-matrices | |
| Inverse M-Matrices | Singular Inverse M-matrices (TCIM-matrices) | |
| Symmetric Inverse M-matrices | ||
| P-Matrices | P0-Matrices | P0,1-Matrices |
| Positive (Nonnegative) P-matrices | Nonnegative P0 (nnP0)-matrices | |
| Sign symmetric P (ssP) Matrices | Sign-symmetric P0 (ssP0) Matrices | Sign Symmetric P0,1-Matrices |
| Weakly sign symmetric P (wssP) Matrices | Weakly sign symmetric P0 (wssP0) Matrices | Weakly Sign Symmetric P0,1-Matrices |
If the class you want is not linked, e-mail
for information.
The one-to-two page PDF files for individual
classes
contain the following information:
Status: summary of current state of knowledge (e.g., done, little progress, etc.) Definition of the class of matrices. Definition of a partial matrix in the class Results: more detailed description of what is known, including citations to references. Examples of digraph or graph diagrams, having completion and not having completion. On the diagram, a vertex v with (v,v) included in the pattern (a specified vertex) is indicated by a solid black dot and a vertex v with (v,v) omitted from the pattern (an unspecified vertex) will be indicated by a hollow circle. For a symmetric class, only positionally symmetric patterns are relevant, and diagrams are graph diagrams; otherwise they are digraph diagrams. In a digraph, when both arcs (v,w) and (w,v) are present in a digraph, the arrows can be omitted, and this is represented by a double line. Thus for a positionally symmetric pattern for a nonsymmetric class a digraph diagram with double edges is used. References
This page is designed and maintained by Leslie Hogben with
contributions
from Luz DeAlba, Amy Wangsness, and Shaun Fallat.
Please e-mail any corrections, suggestions or contributions to lhogben@iastate.edu
