Cayley's hyperdeterminant, the principal minors of a symmetric matrix and the entropy region of 4 Gaussian random variables
Abstract
It has recently been shown that there is a connection between Cayley's hypdeterminant and the principal minors of a symmetric matrix. With an eye towards characterizing the entropy region of jointly Gaussian random variables, we obtain three new results on the relationship between Gaussian random variables and the hyperdeterminant. The first is a new (determinant) formula for the 2×2×2 hyperdeterminant. The second is a new (transparent) proof of the fact that the principal minors of an ntimesn symmetric matrix satisfy the 2 × 2 × .... × 2 (n times) hyperdeterminant relations. The third is a minimal set of 5 equations that 15 real numbers must satisfy to be the principal minors of a 4×4 symmetric matrix.
Additional Information
© 2008 IEEE. Issue Date : 23-26 Sept. 2008; Date of Current Version : 04 March 2009. This work was supported in part by the National Science Foundation through grant CCF-0729203, by the David and Lucille Packard Foundation, by the Office of Naval Research through a MURI under contract no. N00014-08-1-0747, and by Caltech's Lee Center for Advanced Networking.Attached Files
Published - Shadbakht2008p82102008_46Th_Annual_Allerton_Conference_On_Communication_Control_And_Computing_Vols_1-3.pdf
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Additional details
- Eprint ID
- 19160
- Resolver ID
- CaltechAUTHORS:20100722-101032699
- NSF
- CCF-0729203
- David and Lucile Packard Foundation
- Office of Naval Research (ONR)
- N00014-08-1-0747
- Caltech Lee Center for Advanced Networking
- Created
-
2010-07-30Created from EPrint's datestamp field
- Updated
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2021-11-08Created from EPrint's last_modified field
- Other Numbering System Name
- INSPEC Accession Number
- Other Numbering System Identifier
- 10479766