Date of Graduation

Spring 2010

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

Les Reid

Keywords

algebra, matrices, fields, vector spaces, nonsingular subspace

Subject Categories

Mathematics

Abstract

Call a subset of Mn(F) nonsingular if every non-zero element is nonsingular. We develop the background necessary tofind the maximal dimension of nonsingular linear subspaces of Mn(F); which is dependent on the ield. The analysis is conducted over algebraically closed fields, real numbers, rational numbers, andfinite felds. We then develop bounds for the maximal dimension of nonsingular affine subspaces of Mn(F) and singular subspaces of Mn(F) over arbitrar fields.

Copyright

© Stephen Anthony Parry

Campus Only

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