Sparsiication of Rectangular Matrices

Given a rectangular matrix with more columns than rows, nd a base of linear combinations of the row vectors such that these contain as many zero entries as possible. This process is called \sparsiication" (of the matrix). A combinatorial search method to solve sparsiication is presented which needs exponentially many arithmetic operations (in terms of the size of the matrix). However, various properties of the matrix allow a signiicant reduction of the search space, if they apply. In particular, a method to detect and exploit the non-trivial block structure of the matrix is presented. The block method is based on the notion of the generalized inverse, which is deened over arbitrary base elds. The complexity of sparsiication is related to the known open problem of coding theory called \minimalweight of a block code". Two examples are presented to show applications of our methods. Abstract properties of linear dependency , Generalized inverse, Pseudoinverse, Moore-Penrose inverse, Good bases for algebraic number elds, Stewart platform kinematics grant DFG Vo 287/5-2 (Graduiertenkollleg \Beherrschbarkeit komplexer Systeme") y formerly supported by grant DFG Vo 287/5-2; now at Deutsche Telekom AG, Bonn.