# Math 110

## Linear Algebra

Lectures MWF 13:10-14:00, 2050 Valley LSB

Office hours Tu 18:00-20:00, SLC, and by appt.

#### Topics covered

• 08/26: Logistics of the course. Number systems. Fields.
• 08/28: Vector spaces.
• 08/31: Subspaces.
• 09/02: Spanning. Linear dependence/independence.
• 09/04: Bases.
• 09/07: Labor Day. No class.
• 09/09: Dimension.
• 09/11: Linear maps.
• 09/14: Null spaces and ranges.
• 09/16: Matrix representations.
• 09/18: Invertibility.
• 09/21: Midterm #1.
• 09/23: Isomorphism.
• 09/25: Products of vector spaces.
• 09/28: Quotients of vector spaces.
• 09/30: Duality I.
• 10/02: Duality II.
• 10/05: Polynomials.
• 10/07: Invariant subspaces.
• 10/09: Eigenvalues and eigenvectors.
• 10/12: Eigenvectors and upper-triangular matrices.
• 10/14: Eigenspaces and diagonal matrices.
• 10/16: Inner products and norms.
• 10/19: Orthonormal bases.
• 10/21: Orthogonal complements.
• 10/23: Minimization problems.
• 10/26: Midterm #2.
• 10/30: Normal operators.
• 11/02: The real and complex spectral theorems.
• 11/04: Positive operators and isometries.
• 11/06: Polar decomposition.
• 11/09: Singular value decomposition.
• 11/11: Veterans' Day. No class.
• 11/13: Generalized eigenvectors and nilpotent operators.
• 11/16: Decomposition of an operator.
• 11/18: The Cayley-Hamilton Theorem.
• 11/20: The minimal polynomial.
• 11/23: Jordan Form.
• 11/25: No class - pre-Thanksgiving Day.
• 11/30: Operators on real inner product spaces.
• 12/02: Trace.
• 12/04: Determinant.

### Resources

The instructor welcomes cooperation among students and the use of books and online information. However, handing in homework that makes use of other people's work (be it from a fellow student, a book or paper, online source or whatever) without explicit acknowledgement is considered academic misconduct.

### Assignments

All assignments for this class are posted on its Piazza page.

### Solutions

All solutions are also posted on the class Piazza page.

### Exams

First midterm 09/21/15. Second midterm 10/26/15. Final 12/16/15.