2 Basics of Linear Algebra

The mention of "linear algebra" immediately conjures up columns and arrays of numbers. But the relevance of this field goes much beyond recipes for shuffling and combining lists of numbers. Fundamentally, linear algebra comes into play whenever we deal with a collection of objects for which addition makes some sense. For example, two sounds can superpose to make another, two chemical solutions can be mixed together, and two images may be overlaid to make another. Linear algebra studies the representation of such objects and the transformations between them. Only in that context do the columns and arrays of numbers become important. The next section illustrates how linear systems analysis can connect phenomena from radically different parts of biology.