Geometric Properties of Grassmannian Frames for Open image in new window and Open image in new window
Grassmannian frames are frames satisfying a min-max correlation criterion. We translate a geometrically intuitive approach for two- and three-dimensional Euclidean space ( Open image in new window and Open image in new window ) into a new analytic method which is used to classify many Grassmannian frames in this setting. The method and associated algorithm decrease the maximum frame correlation, and hence give rise to the construction of specific examples of Grassmannian frames. Many of the results are known by other techniques, and even more generally, so that this paper can be viewed as tutorial. However, our analytic method is presented with the goal of developing it to address unresovled problems in Open image in new window -dimensional Hilbert spaces which serve as a setting for spherical codes, erasure channel modeling, and other aspects of communications theory.
KeywordsHilbert Space Information Technology Euclidean Space Geometric Property Quantum Information
- 11.Lay DC: Linear Algebra and Its Applications. Addison-Wesley, Boston, Mass, USA; 2003.Google Scholar
- 15.Rosenfeld M: In praise of the Gram matrix. In The Mathematics of Paul Erdős, II, Algorithms and Combinatorics. Volume 14. Springer, Berlin, Germany; 1997:318-323.Google Scholar