Accession Number:

ADP007105

Title:

Singular Values of Large Matrices Subject to Gaussian Perturbation,

Descriptive Note:

Corporate Author:

AT AND T BELL LABS MURRAY HILL NJ

Personal Author(s):

• Denby, Lorraine
• Mallows, Colin

Report Date:

1992-01-01

Pagination or Media Count:

4.0

Abstract:

Extending the work of Wachter 1978, 1980 and many others, we study the configuration of the singular values s.v.s of an a by b matrix of the form X M sigma Z where M is a constant matrix, and the elements of Z are i.i.d., standard Gaussian, in the limit as a and b increase in constant ratio. We put N a b and suppose a alpha N, b Beta N, with sigma of order 1 square root of N. Let the empirical distribution of the s.v.s of X be GN, and let the corresponding moment-generating-function m.g.f be gNt. These are random quantities their distributions depend only on sigma and the empirical distribution Fn of the s.v.s of M. We derive a differential equation that governs the evolution of EgN as sigma increases. In the limit as N yields infinity we can solve this equation and hence exhibit the limiting non-random g itself. This study was motivated by some blood-pressure data collected by a new type of transducer. It suggests a novel way of adjusting large matrices to reduce the effect of additive contamination.

Descriptors:

• *MATRICES(MATHEMATICS)
• *ALGORITHMS
• ADDITIVES
• BLOOD PRESSURE
• CONFIGURATIONS
• CONSTANTS
• CONTAMINATION
• DIFFERENTIAL EQUATIONS
• DISTRIBUTION
• EQUATIONS
• FUNCTIONS
• MOMENTS
• SQUARE ROOTS
• STANDARDS
• TRANSDUCERS
• VALUE

Subject Categories:

• Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE