Matrix Algebra

Matrix Algebra

This course will teach you the basics of vector and matrix algebra and operations necessary to understand multivariate statistical methods, including the notions of the matrix inverse, generalized inverse and eigenvalues and eigenvectors.

This course will teach you the basics of vector and matrix algebra and operations necessary to understand multivariate statistical methods, including the notions of the matrix inverse, generalized inverse and eigenvalues and eigenvectors.

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Overview

Statistics deals with collections of data organized in 1,2,3 or more dimensions. Matrix notation is the best way to compactly represent such data. This course provides the basics of vector and matrix algebra and operations necessary to understand multivariate statistical methods including the matrix inverse, generalized inverse and eigenvalues and eigenvectors.

Learning Outcomes

Students who complete this course will be introduced to vectors and matrices, matrix inverse and linear equations, Eigenvalues and Eigenvectors, and symmetric matrices. It is designed to be a refresher, or an introduction to matrix methods for anyone interested in multivariate statistics, modeling, designing experiments or data mining.

  • Define scalars, vectors, matrices and arrays, and use proper notation
  • Conduct vector and matrix operations
  • Calculate order and rank for a matrix
  • Find the eigenvalues and eigenvectors of a real, square matrix
  • Solve a system of linear equations and the generalized inverse

Who Should Take This Course

Matrix algebra is used heavily in multivariate statistics, and the theory behind many statistical modeling procedures. Matrix notation is used even more widely. If you are interested in taking courses in multivariate statistics, modeling, design of experiments, data mining or other topics involving multivariate data and need a refresher in, or introduction to matrix methods, you should take this course.

Instructors

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Dr. Robert LaBudde

Dr. Robert LaBudde is president and founder of Least Cost Formulations, Ltd., a mathematical software development company specializing in optimization and process control software for manufacturing companies. He has served on the faculties of the University of Wisconsin, Massachusetts Institute of Technology, Old Dominion University and North Carolina State University. Dr. LaBudde is currently Adjunct Professor of Statistics at Old Dominion University.
See Instructor Bio

Course Syllabus

Week 1

Introduction to Vectors and Matrices

  • Notation
  • Definitions of scalars, vectors, matrices and arrays
  • Vector and matrix operations and the transpose
  • Inner and outer products
  • Zero and Identity matricesMatrix multiplication
  • Order and rank of a matrix
  • Length, norm and distance
  • Angle between two vectors, orthogonality

Week 2

Matrix Inverse & linear Equations

  • Order and rank of a matrix
  • Elementary row and column operations
  • Row and column echelon forms
  • Inverse of a square matrix
  • Applications to statistics
  • Linear combinations, dependence and independence
  • More on the rank of a matrix
  • The generalized inverse
  • Homogeneous equations
  • Solving a system of linear equations and the generalized inverse
  • Determinant of a square matrix
  • Applications of determinants in statistics

Week 3

Eigenvalues and Eigenvectors

  • The characteristic equation and eigenvalues and eigenvectors of a real, square matrix
  • Finding eigenvalues and eigenvectors of a matrix
  • Geometric interpretation

Week 4

Symmetric matrices

  • Symmetric matrices
  • Positive definite, semi-definite and non-negative definite matrices
  • Eigenvalues and eigenvectors of a real symmetric matrix
  • The spectral decomposition of a symmetric matrix
  • Principal components analysis
  • Quadratic forms
  • Applications to statistics

Class Dates

2019

Aug 16, 2019 to Sep 13, 2019

2020

Mar 27, 2020 to Apr 24, 2020

Aug 14, 2020 to Sep 10, 2020

2021

No classes scheduled at this time.

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Prerequisites

You should be familiar with intermediate or college algebra, including solving systems of linear equations.

Introductory Statistics

We assume you are versed in statistics or have the equivalent understanding of topics covered in our Statistics 1 and Statistics 2 courses. but do not require them as eligibility to enroll in this course. Please review the course description for each of our introductory statistics courses, estimate which best matches your level of understanding of the material covered in these courses, then take the short assessment test for that course. If you can not answer more than half of the questions correctly, we suggest you take our Statistics 1 and Statistics 2 courses prior to taking this course.

The additional preparation found in Introduction to Statistics 3 – Regression and ANOVA is also helpful.

What Our Students Say​

This is a very well prepared course. The instructor not only pointed out the right book for statisticians but also provided very useful lecture notes that helped a lot

Elena Rose
Data Scientist, NinthDecimal

The instructor, Dr. LaBudde was highly effective.  His written lectures contributed greatly to my understanding and his patient and lengthy answers to my at times overly general questions were extremely informative.  It would be hard or impossible to get this information on my own

Milan Hejtmanek
Seoul National University

Frequently Asked Questions

Can I transfer or withdraw from a course?

We have a flexible transfer and withdrawal policy that recognizes circumstances may arise to prevent you from taking a course as planned. You may transfer or withdraw from a course under certain conditions.

  • Students are entitled to a full refund if a course they are registered for is canceled.
  • You can transfer your tuition to another course at any time prior to the course start date or the drop date, however a transfer is not permitted after the drop date.
  • Withdrawals on or after the first day of class are entitled to a percentage refund of tuition.

Please see this page for more information.

Who are the instructors at the Institute?

The Institute has more than 60 instructors who are recruited based on their expertise in various areas in statistics. Our faculty members are:

  • Authors of well-regarded texts in their area;
  • Advisory board members;
  • Senior faculty; and
  • Educators who have made important contributions to the field of statistics or online education in statistics.

The majority of our instructors have more than five years of teaching experience online at the Institute.

Please visit our faculty page for more information on each instructor at The Institute for Statistics Education.

Please see our knowledge center for more information.

What type of courses does the Institute offer?

The Institute offers approximately 80 courses each year. Topics include basic survey courses for novices, a full sequence of introductory statistics courses, bridge courses to more advanced topics. Our courses cover a range of topics including biostatistics, research statistics, data mining, business analytics, survey statistics, and environmental statistics.

Please see our course search or knowledge center for more information.

Do your courses have for-credit options?

Our courses have several for-credit options:

  • Continuing education units (CEU)
  • College credit through The American Council on Education (ACE CREDIT)
  • Course credits that are transferable to the INFORMS Certified Analytics Professional (CAP®)

Please see our knowledge center for more information.

Is the Institute for Statistics Education certified?

The Institute for Statistics Education is certified to operate by the State Council of Higher Education for Virginia (SCHEV). For more information visit: http://www.schev.edu

Please see our knowledge center for more information.

Visit our knowledge base and learn more.

FAQs + Knowledge Base

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Additional Course Information

Organization of Course

This course takes place online at The Institute for 4 weeks. During each course week, you participate at times of your own choosing – there are no set times when you must be online. Course participants will be given access to a private discussion board. In class discussions led by the instructor, you can post questions, seek clarification, and interact with your fellow students and the instructor.

At the beginning of each week, you receive the relevant material, in addition to answers to exercises from the previous session. During the week, you are expected to go over the course materials, work through exercises, and submit answers. Discussion among participants is encouraged. The instructor will provide answers and comments, and at the end of the week, you will receive individual feedback on your homework answers.

Time Requirements

This is a 4-week course requiring 10-15 hours per week of review and study, at times of your choosing.

Homework

Homework in this course consists of guided numerical problems to test the concepts.

In addition to assigned readings, this course also has the instructor’s expert write-ups on important concepts.

Course Text

All course materials will be provided in the course.

For those who wish additional resources, a recommended text is Matrix Algebra: An Introduction by Krishnan Namboodiri from Sage. Sage Publication offers discounts to students at Statistics.com for many of their titles when the code S06SC is used during checkout on their website (the “0” is a zero not an alphabetical “O”). If you are located in Asia, the web procedure for your location may not accept this discount, try calling your regional Sage representative.

Software

There is no requirement for software in this course. All of the assignments can be done by hand. However, the text illustrates some examples using SAS and the course notes using Microsoft Excel and R.

Software Uses and Descriptions | Available Free Versions
To learn more about the software used in this course, or how to obtain free versions of software used in our courses, please read our knowledge base article “What software is used in courses?” 

Course Fee & Information

Enrollment
Courses may fill up at any time and registrations are processed in the order in which they are received. Your registration will be confirmed for the first available course date unless you specify otherwise.

Transfers and Withdrawals
We have flexible policies to transfer to another course or withdraw if necessary.

Group Rates
Contact us to get information on group rates.

Discounts
Academic affiliation?  In most courses you are eligible for a discount at checkout.

New to Statistics.com?  Click here for a special introductory discount code.  

Invoice or Purchase Order
Add $50 service fee if you require a prior invoice, or if you need to submit a purchase order or voucher, pay by wire transfer or EFT, or refund and reprocess a prior payment.

Options for Credit and Recognition

This course is eligible for the following credit and recognition options:

No Credit
You may take this course without pursuing credit or a record of completion.

Mastery or Certificate Program Credit
If you are enrolled in mastery or certificate program that requires demonstration of proficiency in this subject, your course work may be assessed for a grade.

CEUs and Proof of Completion
If you require a “Record of Course Completion” along with professional development credit in the form of Continuing Education Units (CEU’s), upon successfully completing the course, CEU’s and a record of course completion will be issued by The Institute upon your request.

INFORMS-CAP
This course is recognized by the Institute for Operations Research and the Management Sciences (INFORMS) as helpful preparation for the Certified Analytics Professional (CAP®) exam and can help CAP® analysts accrue Professional Development Units to maintain their certification.

Supplemental Information

There is no supplemental content for this course.

Miscellaneous

There is no additional information for this course.

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Matrix Algebra
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