Linear algebra is an extremely powerful tool, one that can be approached in several ways. Mathematicians see it in terms of vector spaces and linear maps, in which the linear maps are represented by square arrays of numbers, or matrices. For many economists, this theoretical approach seems abstract and hard to relate to. For a practitioner, what matters most is learning to handle tables of numbers, most often drawn from empirical observations. The basic definitions and properties of matrix algebra can then be illustrated through very concrete, easily accessible situations found in the world of economics.
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Order and price matrices
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That day, three customers of a company want to buy four products, some of them in multiple quantities. An order table can then be represented by a matrix, in which the rows correspond to the customers while the columns correspond to the various products available for purchase. Here is matrix C:
