# Spring 2023 - MATH 232 D400

## Overview

• #### Course Times + Location:

Mo, We, Fr 1:30 PM – 2:20 PM
SRYC 5280, Surrey

• #### Exam Times + Location:

Apr 17, 2023
12:00 PM – 3:00 PM
SRYE 1002, Surrey

• #### Instructor:

Abraham Punnen
apunnen@sfu.ca
1 778 782-7611
• #### Prerequisites:

MATH 150 or 151 or MACM 101, with a minimum grade of C-; or MATH 154 or 157, both with a grade of at least B.

## Description

#### CALENDAR DESCRIPTION:

Linear equations, matrices, determinants. Introduction to vector spaces and linear transformations and bases. Complex numbers. Eigenvalues and eigenvectors; diagonalization. Inner products and orthogonality; least squares problems. An emphasis on applications involving matrix and vector calculations. Students with credit for MATH 240 may not take this course for further credit. Quantitative.

#### COURSE DETAILS:

Topics Outline:  Linear equations, matrices, determinants. Introduction to vector spaces and linear transformations and bases. Complex numbers. Eigenvalues and eigenvectors; diagonalization. Inner products and orthogonality; least squares problems. An emphasis on applications involving matrix and vector calculations.

Topic Details:

Vectors
• Vectors in Euclidean n-Space
• Dot Product and Orthogonality
• Lines and Planes
Systems of Linear Equations
• Row Reduction (Gaussian elimination) to Echelon form
• The Geometry of Linear Systems
• Applications in business, science and engineering
Matrices
• Matrix operations
• Matrix inverse; and properties of matrices
• Elementary matrices and calculating matrix inverses
• Matrices with special forms.
Linear Transformations
• Matrices as transformations
• Geometry of Linear Transformations
• Kernel and range
• Composition and Invertibility
• Application to Computer Graphics (optional)
Determinants
• Calculating determinants
• Properties of determinants
• Cramer's rule (optional)
Complex Numbers
• Arithmetic in Cartesian co-ordinates.
• The complex plane, complex conjugate, magnitude and argument (phase).
• Polar form, De Moivre's formula and Euler's formula.
Eigenvalues and Eigenvectors
• Properties and geometry
• Complex eigenvalues and complex eigenvectors
• Dynamical Systems and Markov Chains
• Application to Economics: the Leontief model (optional)
• The Power Method; Application to Internet Search Engines
• Matrix Similarity and Diagonalization
Subspaces of R^n
• Subspaces and Linear Independence
• Basis and Dimension
• The Fundamental Spaces of a Matrix
• Rank
• Change of basis
Orthogonality
• Projection
• Orthogonal bases and the Gram Schmidt process
• Orthogonal matrices (optional)
• Application to least squares approximation

• Assignments 20%
• Midterms (2, 15% each) 30%
• Final Exam 50%

#### NOTES:

THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION.
Students should be aware that they have certain rights to confidentiality concerning the return of course papers and the posting of marks.
Please pay careful attention to the options discussed in class at the beginning of the semester.

#### REQUIREMENTS:

This course is delivered in person, on campus. Should public health guidelines recommend limits on in person gatherings, this course may include virtual meetings. As such, all students are recommended to have access to strong and reliable internet, the ability to scan documents (a phone app is acceptable) and access to a webcam and microphone (embedded in a computer is sufficient).

## Materials

An Introduction to Linear Algebra
Daniel Norman and Dan Wolczuk
3rd Edition
Pearson

The SFU Bookstore will stock both the hardcopy and the electronic version of this textbook. Students are encouraged to obtain the hardcopy.
ISBN: 987-0-13-468263-1

Introduction to Applied Linear Algebra Vectors, Matrices, and Least Squares
Stephen Boyd and Lieven Vandenberghe

ISBN: 978-1-316-51896-0