Patterned complex-valued matrix derivatives

SAM 2008 - 5th IEEE Sensor Array and Multichannel Signal Processing Workshop

Volumn , Issue , 2008, Pages 293-297

  Hjørungnes, Are ^a   Palomar, Daniel P ^b  

^a UNIVERSITY OF OSLO   (Norway)

^b HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

Adaptive filters; Complex valued matrix; Gradient methods; Jacobian; Linear algebra; Optimization methods

Indexed keywords

ACOUSTIC MICROSCOPES; AMPLITUDE MODULATION; CHEMICAL SENSORS; CHLORINE COMPOUNDS; COMMUNICATION; DERIVATIVES; FUNCTION EVALUATION; MISSILE BASES; SENSOR ARRAYS; SENSORS; SIGNAL PROCESSING;

ADAPTIVE FILTERS; COMPLEX-VALUED MATRIX; COMPLEX-VALUED MATRIX FUNCTIONS; GRADIENT METHODS; ILLUSTRATIVE EXAMPLES; INDEPENDENT VARIABLES; JACOBIAN; LINEAR ALGEBRA; MATRIX FUNCTIONS; MULTICHANNEL SIGNAL PROCESSING; OPTIMIZATION METHODS; PATTERNED MATRICES; SIGNAL PROCESSING FOR COMMUNICATIONS; SIMPLE METHODS;

MATRIX ALGEBRA;

EID: 52949114187     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/SAM.2008.4606875     Document Type: Conference Paper

References (14)

1. A. Hjørungnes and D. Gesbert, "Complex-valued matrix differentiation: Techniques and key results," IEEE Trans. Signal Process., vol. 55, no. 6, pp. 2740-2746, June 2007.
2. J. R. Magnus and H. Neudecker, Matrix Differential Calculus with Application in Statistics and Econometrics. Essex, England: John Wiley & Sons, Inc., 1988.
3. D. A. Harville, Matrix Algebra from a Statistician's Perspective. Springer-Verlag, 1997, corrected second printing, 1999.
4. T. P. Minka, "Old and new matrix algebra useful for statistics," December 28, 2000. [Online]. Available: http://research. microsoft.com/~minka/papers/matrix/
5. D. H. Brandwood, "A complex gradient operator and its application in adaptive array theory," IEE Proc., Parts F and H, vol. 130, no. 1, pp. 11-16, Feb. 1983.
6. M. Brookes. Matrix reference manual. [Online]. Available: http://www.ee,ic.ac.uk/hp/staff/dmb/matrix/intro.html
7. K. Kreutz-Delgado, "The complex gradient operator and the ℂℝcalculus," Dept. of Electrical and Computer Engineering, UC San Diego, Tech, Rep. Course Lecture Supplement No. ECE275A, Sept.-Dec. 2005, http://dsp.uosd.edu/-kreutz/PEI05.html.
8. D. P. Palomar and S. Verdú, "Gradient of mutual information in linear vector Gaussian channels," IEEE Trans. Inform. Theory, vol. 52, no. 1, pp. 141-154, Jan. 2006.
9. D. S. Tracy and K. G. Jinadasa, "Patterned matrix derivatives," The Canadian Journal of Statistics, vol. 16, no. 4, pp. 411-418, 1988.
10. R. A. Horn and C. R. Johnson, Topics in Matrix Analysis. Cambridge University Press Cambridge, UK, 1991, reprinted 1999.
11. A. Hjørungnes and D. Gesbert, "Hessians of scalar functions which depend on complex-valued matrices," in Proc. Int. Symp. on Signal Proc. and Its Applications, Sharjah, United Arab Emirates, Feb. 2007.
12. N. Young, An Introduction to Hilbert Space. The Pitt Building, Trumpington Street, Cambridge: Press Syndicate of the University of Cambridge, 1990, reprinted edition.
13. R. F. Rinehart, "The exponential representation of unitary matrices," Mathematics Magazine, vol. 37, no. 2, pp. 111-112, Mar. 1964.
14. J. R. Barry, E. A. Lee, and D. G. Messerschmitt, Digital Communication, 3rd ed. 3300 AH Dordrecht, The Netherlands: Kluwer Academic Publishers, 2004.