The use of linear algebra in Section 15.4.1 suggests further development of algebraic concepts. This section briefly introduces concepts that resemble ordinary linear algebra but apply to linear combinations of vector fields. This provides the concepts and tools needed to characterize important system properties in the remainder of this section. This will enable the assessment of whether a system is nonholonomic and also whether it is STLC. Many of the constructions are named after Sophus Lie (pronounced ``lee''), a mathematician who in the nineteenth century contributed many ideas to algebra and geometry that happen to be relevant in the study of nonholonomic systems (although that application came much later).