Matrices and Linear Transformations Fall 2016

Administrivia

The course meets MWF 3:30PM-4:20PM in HH B131. Office hours are MWF 2:30-3:20PM in my office, WEH 6130. If you can't make the office hours and want to meet, send email to jcumming@andrew.cmu.edu to arrange an appointment.

Homework will be set most Fridays, will be due on the following Friday, and should be returned graded by the Friday after that. Late homework will not be accepted under any circumstances, but the lowest homework score will be dropped. Homework must be typeset or legibly written in ink, homework that is illegible or written in pencil will be returned ungraded.

Collaboration is cheating and will lead to serious consequences, which can include failing the course and disciplinary action by the university.

Prerequisites and syllabus

Prerequisites: Basic facts about the real numbers. The ability to write and recognise a proof.

Core material in syllabus:

• Real and complex vectors and matrices
• Formulating systems of linear equations as matrix equations, solution by Gaussian eleimination
• Columnspace and rowspace of a matrix, rank and nullity, the rank-nullity theorem
• Inverse matrices and the determinant
• Bases, change of basis
• Linear transformations and their matrices, similarity
• Inner product of vectors, orthonormal bases, Gram-Schmidt process
• Projection to a subspace, orthogonal complement of a subspace, least squares
• Eigenvectors and eigenvalues, diagonalisation
• Symmetric/Hermitian and Orthogonal/Unitary matrices

• Computational aspects
• Bilinear/sesquilinear and quadratic forms
• Jordan normal form of a matrix
• Singular value decomposition of a matrix

Exams, HW and grading policy

There will be a midterm and a final, each of which will have an in-class and a take-home component. Grades will be assigned according to a formula in which (roughly speaking) homework counts 35 percent, the midterm counts 25 percent and the final counts 40 percent.

Homework sets and exams

Homework set and exam solutions

Lecture notes