General Information
Math 350 is a proof-based continuation of Math 250, covering abstract vector spaces and linear transformations, diagonalization, Jordan canonical form, and inner product spaces. Math 350 is one of two courses most mathematics majors may take to satisfy the upper-level algebra requirement. The other is Math 351.
The focus of Math 350 is axiomatic linear algebra, starting from the abstract notions of vector space and of linear transformation. Students will be expected to write precise proofs, building on their proof-writing experience from Math 300. From this abstract viewpoint, linear algebra will be developed far beyond Math 250, with new insight and new applications.
The honors section of Math 350 covers the same topics as the non-honors sections, but in significantly greater depth. Enrollment in the honors section requires the approval of the Honors Advisor.
Prerequisites
- Math 250, Introductory Linear Algebra
- and a C or better in Math 300, Mathematical Reasoning
- and Math 251, or Math 291, Multivariable Calculus
Enrollment in the honors section requires the approval of the Honors Advisor.
Textbook
For current textbook please refer to our Master Textbook List page
General Syllabus
Topics, in approximate sequence:
- Review of the basic ideas and techniques of Math 250
- Abstract vector spaces
- Subspaces; span of subsets; linear independence
- Bases and dimension
- Linear transformations; matrix representation
- Composition of linear transformations; invertibility
- Change-of-coordinate matrices (change of basis)
- Theoretical aspects of systems of linear equations
- Determinants and their properties
- Eigenvalues and eigenvectors; the characteristic polynomial
- Diagonalizability
- Invariant subspaces; the Cayley-Hamilton Theorem
- Jordan canonical form
- Real and complex inner product spaces
- Normal and self-adjoint matrices; unitary and orthogonal matrices
Instructors have some flexibility in deciding which proofs to treat.
As time allows, with the instructor’s discretion, some subset of the following topics may also be covered: Dual spaces, Direct sums of subspaces, Minimal polynomial, Rational canonical form, Normal and self-adjoint operators, Bilinear and quadratic forms, Applications of the theory.