Characterizing injectivity of classes of maps via classes of matrices
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Characterizing injectivity of classes of maps via classes of matrices. / Feliu, Elisenda; Müller, Stefan; Regensburger, Georg.
In: Linear Algebra and Its Applications, Vol. 580, 31.01.2019, p. 236-261.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Characterizing injectivity of classes of maps via classes of matrices
AU - Feliu, Elisenda
AU - Müller, Stefan
AU - Regensburger, Georg
PY - 2019/1/31
Y1 - 2019/1/31
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
VL - 580
SP - 236
EP - 261
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
SN - 0024-3795
ER -
ID: 218040524