Abstract
PurposeIt is frequently mentioned in literature that LCA is linear, without a proof, or even without a clear definition of the criterion for linearity. Here we study the meaning of the term linear, and in relation to that, the question if LCA is indeed linear.MethodsWe explore the different meanings of the term linearity in the context of mathematical models. This leads to a distinction between linear functions, homogeneous functions, homogenous linear functions, bilinear functions, and multilinear functions. Each of them is defined in accessible terms and illustrated with examples.ResultsWe analyze traditional, matrix-based, LCA, and conclude that LCA is not linear in any of the senses defined.Discussion and conclusionsDespite the negative answer to the research question, there are many respects in which LCA can be regarded to be, at least to some extent, linear. We discuss a few of such cases. We also discuss a few practical implications for practitioners of LCA and for developers of new methods for LCI and LCIA.
Highlights
It is frequently mentioned in literature that LCA is linear, without a proof, or even without a clear definition of the criterion for linearity
This implies that F is a homogeneous linear function when we only study the effect of f1
LCA possesses a weaker property of multilinearity, but only with respects to elements of the final demand vector and the emission data
Summary
It is frequently mentioned in literature that LCA is linear, without a proof, or even without a clear definition of the criterion for linearity. We study the meaning of the term linear, and in relation to that, the question if LCA is linear. We explore the different meanings of the term linearity in the context of mathematical models. This leads to a distinction between linear functions, homogeneous functions, homogenous linear functions, bilinear functions, and multilinear functions. Results We analyze traditional, matrix-based, LCA, and conclude that LCA is not linear in any of the senses defined. Despite the negative answer to the research question, there are many respects in which LCA can be regarded to be, at least to some extent, linear.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
