  The existence and uniqueness conditions are a prerequisite for reliable
reconstruction of sparse signals from reduced sets of measurements within the
Compressive Sensing (CS) paradigm. However, despite their underpinning role for
practical applications, existing uniqueness relations are either
computationally prohibitive to implement (Restricted Isometry Property), or
involve mathematical tools that are beyond the standard background of
engineering graduates (Coherence Index). This can introduce conceptual and
computational obstacles in the development of engineering intuition, the design
of suboptimal practical solutions, or understanding of limitations. To this
end, we introduce a simple but rigorous derivation of the coherence index
condition, based on standard linear algebra, with the aim to empower signal
processing practitioners with intuition in the design and ease in
implementation of CS systems. Given that the coherence index is one of very few
CS metrics that admits mathematically tractable and computationally feasible
calculation, it is our hope that this work will help bridge the gap between the
theory and applications of compressive sensing.
