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Gaussian families and a theorem on patterned matrices

Published online by Cambridge University Press:  14 July 2016

Wayne W. Barrett  and
Philip J. Feinsilver
Wayne W. Barrett*
Affiliation:
University of Wisconsin-Madison
Philip J. Feinsilver*
Affiliation:
University of Utah
*
∗Now at Texas A&M University.
∗∗Now at Southern Illinois University.
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Abstract

In this paper we use the properties of the covariance matrix of a Gaussian Markovian family to give a probabilistic proof of a theorem about inverses of tridiagonal matrices.

Keywords

COVARIANCE MATRIXGAUSSIAN FAMILYMARKOV PROPERTY

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 3 , September 1978 , pp. 514 - 522
Copyright
Copyright © Applied Probability Trust 1978 

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References

Feller, W. (1971) An Introduction to Probability Theory and its Applications, Vol. 2, 2nd edn, Wiley, New York, 85–86.Google Scholar
Gantmakher, F. R. and Krein, M. G. (1950) Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems, 2nd edn, 118. Translated from a publication of the State Publishing House for Technical-Theoretical Literature, Moscow-Leningrad, 1950. United States Atomic Energy Commission, Office of Technical Information.Google Scholar
Graybill, F. A. (1969) Introduction to Matrices with Applications in Statistics, p. 179. Wadsworth Publishing Company, Belmont, California.Google Scholar