Department of Mathematics and Statistics
MATH 2135, Linear Algebra
Winter 2017
Peter Selinger

Updates are shown in red.

Course Description: This course is a continuation of Math 2030 with an emphasis on foundations and the theory of vector spaces and linear transformations. Additional topics include inner product spaces, symmetric and orthogonal transformations, bilinear forms, similarity and diagonalization, the solution of linear differential equations, and various applications in mathematics, physics and computer science.

Instructor: Prof. Peter Selinger
Department of Mathematics and Statistics
Chase Building, Room 303
Email: (please mention "2135" in the subject line)
Lectures: TTh 11:30-1, LSC C334
Website: Updated information, assignments, any handouts, etc., will be available from
Office Hours: Mondays 10:30-11:30.
Prerequisites: Prerequisites: Math 2030 and Math 1000.
Exclusions: Math 2040.
Textbook: Seymour Lipschutz and Marc Lipson. Schaum's Outlines on Linear Algebra. 5th edition, McGraw-Hill, 2012.
Topics: Field axioms, elementary properties of fields. Review of systems of linear equations. Vector space axioms. Examples of vector spaces. Linear combinations and span, subspace axioms, intersection of subspaces. Linear dependence and independence, bases, replacement lemma, dimension. Linear functions, kernel and image, rank and nullity, dimension theorem. Matrix of a linear map, change of basis matrix. Determinants. Complex numbers. Inner product spaces, Cauchy Schwarz inequality. Orthogonal and orthonormal sets, Gram-Schmidt orthogonalization procedure. Unitary and orthogonal matrices. Eigenvectors, eigenvalues, and diagonalization. Algebraic and geometric multiplicity. Diagonalization of hermitian matrices. Solution of linear differential equations.
Course Work: There will be an in-class midterm and a final exam. The midterm is scheduled for Thursday, March 2 in class. The final exam will be scheduled by the registrar's office. There will also be weekly homework, to be handed in at the beginning of class on Thursdays. From each homework set, I will choose some number of problems that will be graded. Late homework will not be accepted except with my prior permission. Each week, you will also be assigned some reading from the textbook.
Marks: Marks will be based on the homework, midterm, and final exam. Class participation may be taken into account. The homework counts 25%, the midterm counts 25%, and the final exam counts 50%. You need to pass the final exam in order to pass the course. Numerical grades are converted to letter grades via the Dalhousie Common Grade Scheme: 90–100 = A+, 85–89.9 = A, 80–84.9 = A−, 77–79.9 = B+, 73–76.9 = B, 70–72.9 = B−, 65–69.9 = C+, 60–64.9 = C, 55–59.9 = C−, 50–54.9 = D, 0–49.9 = F.
Missed test policy: A missed midterm cannot be written at another time. If you miss the midterm without my prior permission, then it will count as a 0. Exceptions are made in two cases: (1) if you obtain my prior permission to miss a midterm, or (2) if you have an officially valid excuse such as a medical doctor's note. In these cases, the weight of the missed midterm will be shifted to the final exam (i.e., the final exam will then count 75% instead of 50%). A missed final exam can only be made up if there is a valid medical excuse.
Note taker sought: A note taker is required to assist a student in this class. There is an honorarium with some conditions. If you are interested, please go to the Advising and Access Services Centre, Killam G28 for more information or send an email to
Policies: For Dalhousie's policies on accommodation, academic integrity, copyright, student code of conduct, and for a list of services available to students, see here.

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