TY - GEN A1 - Benner, Peter A1 - Byers, Ralph T1 - An Arithmetic for Matrix Pencils: Theory and New Algorithms N2 - This paper introduces arithmetic-like operations on matrix pencils. The pencil-arithmetic operations extend elementary formulas for sums and products of rational numbers and include the algebra of linear transformations as a special case. These operation give an unusual perspective on a variety of pencil related computations. We derive generalizations of monodromy matrices and the matrix exponential. A new algorithm for computing a pencilarithmetic generalization of the matrix sign function does not use matrix inverses and gives an empirically forward numerically stable algorithm for extracting deflating subspaces. Y1 - 2004 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/132 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-1323 ER -