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# Accession Number:

## ADA114494

# Title:

## Structure of Invertible (BI) Infinite Totally Positive Matrices.

# Descriptive Note:

## Technical summary rept.,

# Corporate Author:

## WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

# Report Date:

## 1981-12-01

# Pagination or Media Count:

##
20.0

# Abstract:

## An l subinfinity-invertible nonfinite totally positive matrix A is shown to have one and only one main diagonal. This means that exactly one diagonal of A has the property that all finite sections of A principal with respect to this diagonal are invertible and their inverses converge boundedly and entrywise to A to the -1 power. This is shown to imply restrictions on the possible shapes of such a matrix. In the proof, such a matrix is also shown to have a l subinfinity invertible LDU factorization. In addition, decay of the entries of such a matrix away from the main diagonal is demonstrated. It is also shown that a bounded sign-regular matrix carrying some bounded sequence to a uniformly alternating sequence must have all its columns in c sub o. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#