A or I-A? Unifying the computational structures of process- and IO-based LCA for clarity and consistency

Why are both A-1${\mathbf{A}}<^>{-1}$ and (I-A)-1${(\mathbf{I}-\mathbf{A})}<^>{-1}$ used in life cycle assessment (LCA) matrix computations? This is a question that, in our experience of teaching LCA, students often wonder about and struggle with. A brief survey of the literature suggests that the question can also confuse experienced LCA practitioners. Here, we seek to unify the computational structures of the two LCA approaches to achieve greater clarity and consistency, especially to make them easier to teach. We first show how small but crucial differences in the set-up of the two approaches lead to the use of A$\mathbf{A}$ versus I-A$\mathbf{I}-\mathbf{A}$. Then, we discuss the options to unify the presentations in a coherent way. We do not prescribe one way or the other. A larger point we hope to stress is the importance of unification, which may have both pedagogical and methodological benefits.

Automated summary

Why are both A-1 and (I-A)-1 used in life cycle assessment (LCA) matrix computations? In this article, the authors aim to unify the computational structures of the two approaches to achieve greater clarity and consistency.