The dual viewpoint from structural analysis and dimensional analysis, as previewed in §1.2, is explained in more detail. Firstly, two different kinds, “accurate” and “inaccurate,” are distinguished among numbers characterizing real-world systems, and secondly, algebraic implications of the principle of dimensional homogeneity are discussed. These observations lead to the concepts of “mixed matrices,” “mixed polynomial matrices,” and “physical matrices” as the mathematical models of matrices arising from real problems.