# Linear Functions

In function notation \(f: \mathbf{R}^n \to \mathbf{R}\) means that \(f\) is a function that maps real \(n\)-vectors to real numbers, it is a scalar-valued function of \(n\)-vectors. In other words, if \(x\) is an \(n\)-vector, then \(f(x)\), which is a scalar, denotes the value of \(f\) at \(x\). That is, \(f\) returns a real number. Furthermore, we can interpret \(f\) as a function of \(n\) scalar arguments, as in …