Date of Graduation
Master of Science in Mathematics
algebra, matrices, fields, vector spaces, nonsingular subspace
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.
© Stephen Anthony Parry
Parry, Stephen Anthony, "Maximum Dimension Of Nonsingular Subspaces Of Mn(F)" (2010). MSU Graduate Theses. 2923.