M311 LINEAR ALGEBRA AND MATRIX THEORY

Prerequisite and degree relevance:

This course has been replaced by M341.

The prerequisite is M408D or the equivalent or consent of instructor. (Credit may not be

received for both M311 and M340L. M311 is required for math majors; furthermore,

math majors must make a grade of at least C in M311.)

Course description:

The emphasis in this course is on understanding the concepts and learning to use the tools

of linear algebra and matrices. Some time should be devoted to teaching students to do

proofs. The fundamental concepts and tools of the subject covered are:

Matrices:

matrix operations, the rules of matrix algebra, invertible matrices.

Linear equations:

row operations and row equivalence; elementary matrices; solving ystems of linear

equations by Gaussian elimination; inverting a matrix with the aid of row operations.

Vector spaces:

vector spaces and subspaces; linear independence and span of a set of vectors, basis and

dimension; the “standard” bases for common vector spaces.

Inner product spaces:

Cauchy-Schwarz inequality, orthonormal bases, the Gramm-Schmidt procedure,

orthogonal complement of a subspace, orthogonal projection.

Linear Transformations:

kernel and range of a linear transformation, the Rank- Nullity Theorem, linear

transformations and matrices, change of basis, similarity of matrices.

Determinants:

the definition and basic properties of determinants, Cramer’s rule.

Eigenvalues:

eigenvalues and eigenvectors, diagonalizability of a real symmetric matrix, canonical

forms.