Abstract Linear Algebra

An introduction to the theory of linear algebra starting with vector spaces. Subspaces, bases, dimension. Linear transformations, invariant subspaces, eigenvalues, eigenspaces, and diagonalizing linear operators. Inner product spaces and orthogonal projections. The emphasis will, in general, be on proofs rather than computation. Additional topics may include normal forms, minimal polynomials, determinant of an operator, normal operators over complex vector spaces as well as applications of linear algebra. Recommendations: MATH 34 or 39 or permission of instructor. Students may count only one of MATH 70 and MATH 72 for credit.