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Absolutely determined matrices. (English) Zbl 0712.15025

A real valued matrix \(A=(a_{ij})\) is called determined if \(\min_{i}\max_{j} a_{ij}=\max_{j}\min_{i} a_{ij}=Val A\) holds. A matrix A is said to be absolutely determined if every submatrix of A, including A itself, is determined. Properties of these matrices are studied, namely the one-to-one correspondence between symmetric absolutely determined matrices and so-called quasilinear set functions and some estimates on the number of absolutely determined matrices.
Reviewer: K.Burian

MSC:

15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
06A12 Semilattices
26A51 Convexity of real functions in one variable, generalizations
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References:

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