CONCEPTS FROM GEOMETRY
4.1 Line Segments
In the following analysis we concern ourselves only with n. The elements of this space are the n-component vectors x = [x1, x2,…, xn].
The line segment between two points x and y in n is the set of points on the straight line joining points x and y (see Figure 4.1). Note that if z lies on the line segment between x and y, then
where α is a real number from the interval [0,1]. The equation above can be rewritten as z = αx + (1 − α)y. Hence, the line segment between x and y can be represented as
4.2 Hyperplanes and Linear Varieties
Let u1, u2,…, un, v , where at least one of the ui is nonzero. The set of all points ...