#### Description

The course provides an introduction to linear algebra and matrix theory. It is intended primarily for engineering students. This course cannot be used toward the upper level math requirements for MATH/STAT majors. Credit will be granted for only one of the following: MATH 240, MATH 341, or MATH 461.

#### Prerequisites

MATH 141 and one MATH/STAT course for which MATH 141 is a prerequisite.

#### Topics

**Systems of Linear Equations**

Gaussian elimination

Echelon forms

Existence and uniqueness of solutions

Homogeneous systems

**Matrices**

Addition, scalar multiplication, multiplication of matrices

Elementary matrices and inversion

LU decomposition

Systems of linear equations as matrix equations

*Partitioned matrices

Determinants and their properties

Cramer's rule

**Vector Spaces**

Subspaces and spanning sets

Linear independence

Basis and dimension

Row and column spaces of a matrix

Rank of a matrix

Null space of a matrix

**Linear Transformations**

Kernel and range

Matrix representation

Change of basis and similarity of matrices

**Scalar Products and Orthogonality**

Cauchy-Schwarz and triangle inequalities

Length and angles

Pythagorean theorem

Orthonormal sets

Orthogonal complements of the null space and column space

Orthogonal projection

Least squares problems

Orthogonal matrices

Gram-Schmidt process and QR factorization

**Eigenvalues**

Complex eigenvalues

Diagonalization of matrices

Spectral theorem for symmetric (*hermitian) matrices

*Quadratic forms

Positive definite matrices

*Nonnegative matrices

**Applications to i****nclude several of the following:**

*Liontief Input-Output Model

*Markov Chains

*Computer Graphics

*Least squares data fitting

*Fourier Series

*Systems of Differential Equations

*Difference Equations

*Max-Min Theory for functions of several variables (Hessian Matrix)

**MATLAB use**

In assigned homework through the semester