Mathematical appendix

Summary

This mathematical appendix provides proofs of some theorems in advanced linear algebra and the theory of linear programming. It is assumed that the reader knows the basics of linear algebra as they are presented, for example, in Hadley (1961), Schneider and Barker (1968), or Hoffman and Kunze (1971). In the proofs given the use of parts of mathematics other than linear algebra has been avoided as much as possible; however, it is assumed that the reader knows the language of set theory and some elements of calculus when these concepts are mentioned in the statements to be proved. The idea of requiring the reader to know only some linear algebra in order to be able to read this book was suggested by the teaching experience of one of us: to provide some more advanced linear algebra as a side dish is rather convenient, whereas this simply cannot be done for calculus or topology unless one refrains from providing complete proofs. In our opinion such a procedure would be difficult to defend from a didactical point of view since it leads students into mistaking mathematics for a kind of cookbook in which ready-made recipes can be found, while it should rather be seen as a logical tool developed to master issues too complex to be treated in ordinary language. Due to limitations of space we will not expound basic linear algebra here.