Math 2370 *** MATRICES & LINEAR OPERATORS *** Fall 2008

Instructor: David Swigon

Office: Thackeray 511, 412-624-4689,

Lectures:  MWF 10:00-10:50am, Thackeray 704

Recitations:  Th 10-10:50am, Thackeray 704, Instructor Jonathan Holland

Office Hours: MW 2:00am-3:30pm, Thackeray 511, or by appointment.

Course Web Page: (check frequently for changes and updates)

Course Description

Undergraduate linear algebra courses deal primarily with matrices and their properties, solution of systems of linear equations, eigenvalue analysis. This course covers the basic theory of linear vector spaces and linear transformations using axiomatic approach that builds upon primitive concepts toward more complex ones.


Undergraduate linear algebra or matrix theory.


(Available at The Book Center on Fifth Ave.)

Other recommended books

Beautifully written book that provides brief and to-the-point explanation of the main concepts and their motivations. Should be read alongside of Lax.

Book written from the point of view of abstract algebra. Rich in examples and exercises, covers more than necessary.

Undergraduate level, focuses on matrices, good for first reading or as a refresher.

Grading Scheme

Quizzes: 15%

Homework: 20%

Midterm Exam: 30%

Final Exam: 35%


Tentative syllabus is given below, with a list of assigned reading for the week.

Every Friday a list of practice problems for the next week will be given. The students are expected to work out the practice problems and consult the instructor if difficulties arise. Few times during the term, with advance notice, the problems will be collected and graded as a homework. The approximate schedule and a list of practice problems will be posted below. 

Every Friday the lecture will start with a 20 min quiz based on the material covered since the last quiz. Quizzes will be graded and will count towards the final grade.

The recitations on Thursdays will be spend on the discussion of practice problems assigned for the week, so please come prepared.






Practice problems


Aug 25 - Aug 29

[L] 1

Linear space, linear dependence, basis, dimension, subspace, quotient space

Set I


Sep 1 Labor Day

Sep 2 - Sep 5

[L] 2

Linear functionals, annihilator codimension

Set II

Sep 8 - Sep 12

[L] 3

Linear mappings, domain, nullspace, range, fundamental theorem



Sep 15 - Sep 19

[L] 3

Algebra of linear mappings, transposition, similarity, projections,

Matrices, rank

Set IV is a

HOMEWORK due Sep 19


Sep 22 - Sep 26

[L] 4

Simplices, trace, permutation group

Set V


Sep 29 - Oct 1

[L] 5

Determinant, multiplicative property

Set VI


Oct 6 - Oct 10

[L] 5

Laplace’s expansion, Cramer’s rule, trace

Oct 14



Oct 17

Midterm Exam

Covers [L] 1-5


Oct 20 - Oct 24

[L] 6

Iteration of linear maps, eigenvalues, eigenvectors, characteristic polynomial, Spectral mapping theorem

Set VII is a HOMEWORK due Oct 24


Oct 27 - Oct 29

[L] 6

Cayley-Hamilton theorem, Generalized eigenvectors, minimal polynomial, similarity of matrices



Nov 3 - Nov 7

[L] 7

Scalar product, distance, orthonormal basis, completeness, local compactness

Set IX is a HOMEWORK due Nov 12


Nov 10 - Nov 14

[L] 7

Orthogonal complement, orthogonal projection, adjoint, norm, Isometry, orthogonal groups

Set X

Nov 24


[L] 8

Quadratic forms, spectral resolution,


Dec 1 - Dec 5

[L] 8

commuting maps, Normal maps, Rayleigh quotient,

Set XI


Dec 8

[L] 8

minmax principle

Dec 10





Dec 12


Final Exam

10:00 - 12:00am

Thackeray Rm 704