DocumentCode :
2944465
Title :
Cayley´s hyperdeterminant, the principal minors of a symmetric matrix and the entropy region of 4 Gaussian random variables
Author :
Shadbakht, Sormeh ; Hassibi, Babak
Author_Institution :
Electr. Eng. Dept., California Inst. of Technol., Pasadena, CA
fYear :
2008
fDate :
23-26 Sept. 2008
Firstpage :
185
Lastpage :
190
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 2times2times2 hyperdeterminant. The second is a new (transparent) proof of the fact that the principal minors of an ntimesn symmetric matrix satisfy the 2 times 2 times .... times 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 times 4 symmetric matrix.
Keywords :
Gaussian processes; computational complexity; entropy; matrix algebra; random processes; Cayley hyperdeterminant; Gaussian random variables; entropy region; symmetric matrix; Capacity planning; Contracts; Covariance matrix; Cramer-Rao bounds; Entropy; Equations; Information theory; Probability distribution; Random variables; Symmetric matrices;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Communication, Control, and Computing, 2008 46th Annual Allerton Conference on
Conference_Location :
Urbana-Champaign, IL
Print_ISBN :
978-1-4244-2925-7
Electronic_ISBN :
978-1-4244-2926-4
Type :
conf
DOI :
10.1109/ALLERTON.2008.4797553
Filename :
4797553
Link To Document :
بازگشت