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Linear Relations

Irina Kurbatova
Organization: Voronezh State University
Department: Department of Applied Mathematics and Mechanics
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This is a package that performs some usual operations with linear relations in R^n.

Let X and Y be linear spases. A linear relation [1-4] is a linear subspace W in XxY. A linear relation induces a mutivalued operator A:X ->Y. Namely, they say that y in Ax or y=Ax iff (x,y)in W. Usualy, they do not distiguish between W and A and write (x,y) in A instead of (x,y) in W. Any linear operator can be considered as a linear relation if one identifies the operator with its graph.

Bibliography [1] Arendt W. Approximation of degenerate semigroups. Tubinger Berichte fur Funktionalanalysis. Helf Basel: Birkhauser--Verlag, 2001. [2] Baskakov A. G. and Chernyshov K. I. Spectral theory of linear relations and degenerate semigroups of operators. Mathemat. Sbornik, 2002. Vol. 371, No~11. pp. 3--42 (in Russian). [3] Cross R. Multivalued linear operators. New York: M. Dekker, 1998. [4] Favini A., Yagi A. Degenerate evolution equations in Banach spaces. New York: M. Dekker, 1998.

*Mathematics > Algebra > Linear Algebra

Linear Relation, Multiplication, Addition, Harmonic Addition, Image of zero, Section
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Description_LinearRelations.nb (29.5 KB) - Installation and Usage Instructions [for Mathematica 5.0]
LinearRelations.zip (7.7 KB) - ZIP archive