The need to solve systems of linear equations frequently arises in mathematics, the physical sciences, engineering and economics. In this course we study these systems from an algebraic and geometric viewpoint. Topics include systems of linear equations, matrix algebra, Euclidean vector spaces, linear transformations, linear independence, dimension, eigenvalues and eigenvectors.
- Demonstrate algebraic and geometric understanding of properties of linear systems, matrix algebra, linear independence, dimension, coordinate systems, eigenvalues and eigenspaces, diagonalization, and the spectral theorem.
- Demonstrate sophisticated comprehension of linear transformations and the algebraic and geometric structures of subspaces and linear spaces.
- Formulate and structure mathematical proofs.
- Successfully apply linear algebra concepts to mathematically model and analyze problems of current interest in the sciences, economics, engineering, and technology.