Characterizing injectivity of classes of maps via classes of matrices

TY - JOUR

T1 - Characterizing injectivity of classes of maps via classes of matrices

AU - Feliu, Elisenda

AU - Müller, Stefan

AU - Regensburger, Georg

PY - 2019/11/1

Y1 - 2019/11/1

N2 - We present a framework for characterizing injectivity of classes of maps (on cosets of a linear subspace) by injectivity of classes of matrices. Using our formalism, we characterize injectivity of several classes of maps, including generalized monomial and monotonic (not necessarily continuous) maps. In fact, monotonic maps are special cases of component-wise affine maps. Further, we study compositions of maps with a matrix and other composed maps, in particular, rational functions. Our framework covers classical injectivity criteria based on mean value theorems for vector-valued maps and recent results obtained in the study of chemical reaction networks.

AB - We present a framework for characterizing injectivity of classes of maps (on cosets of a linear subspace) by injectivity of classes of matrices. Using our formalism, we characterize injectivity of several classes of maps, including generalized monomial and monotonic (not necessarily continuous) maps. In fact, monotonic maps are special cases of component-wise affine maps. Further, we study compositions of maps with a matrix and other composed maps, in particular, rational functions. Our framework covers classical injectivity criteria based on mean value theorems for vector-valued maps and recent results obtained in the study of chemical reaction networks.

KW - math.AG

KW - math.CA

KW - 26B10, 15B35, 80A30

U2 - 10.1016/j.laa.2019.06.015

DO - 10.1016/j.laa.2019.06.015

M3 - Journal article

SN - 0024-3795

VL - 580

SP - 236

EP - 261

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -