An Introduction to Econometric Theory

2Matrix Representation

2.1 Systems of Equations

A matrix is a rectangular array whose cells contain numbers, represented in mathematical manipulations by a single symbol. A computer spreadsheet, with rows and columns, is a natural image to have in mind here. The key component of the notation is one already seen in (1.30), the double subscript, where typically, but not invariably, the first subscript indicates the row of the entry and the second indicates the column. The elements and are natural instances, but note that these reverse the usual ordering, if is the row subscript and 1 or 2 the column subscript. In econometrics, this happens!

Consider the case of three rows and three columns:

A convention used in some (but not all) texts is to use a boldface font for the symbol representing a matrix, and also typically a capital letter. Boldface is always used in this book. The elements of a matrix, written as with generic subscripts, are numbers of the usual kind.¹ Sometimes it is convenient ...