Linear Equations and Linear Inequalities

While Chapter 1 reviews general structural aspects of real vector spaces, we now discuss fundamental computational techniques for linear systems in this chapter. For convenience of the discussion, we generally assume that the coefficients of the linear systems are real numbers. It is important to note, however, that in practical computations we mostly deal with rational numbers as input parameters. We therefore point out right at the outset that all the algorithms of this chapter (Gaussian elimination, orthogonal projection, Fourier-Motzkin elimination) will compute rational output quantities if the input parameters are rational numbers, as the reader can easily check.