is nonsingular. Show that f is invertible and that f ^{−1} is a linear-fractional mapping. Give an explicit expression for f^{−1} and its domain in terms of A, b, c, and d. Hint. It may be easier to express f ^{−1} in terms of Q.

2.19 Linear-fractional functions and convex sets. Let f : R^{m} → R^{n} be the linear-fractional function

In this problem we study the inverse image of a convex set C under f, i.e.,

For each of the following sets C ⊆ R^{n}, give a simple ...

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