Matrix Algebra Review

Dr. Robert LaBudde

Aim of Course:

Statistics deals with collections of data organized in 1, 2, 3 or more dimensions. Compactly representing such data is best accomplished by the use of matrix notation, particularly when solutions to optimization (e.g., regression) or estimating (i.e, models) are involved. This course will provide 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. After successfully completing this course, you will be able to use and understand vector and matrix operations and equations, find and use a matrix inverse, and use and understand the eigenset of a symmetric matrix.

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.

For those enrolled in a Program of Advanced Statistical Studies, this is a required or elective course in the following Programs:

• Biostatistics (epidemiology) - elective
• Biostatistics (controlled trials) - elective
• Statistics in Business & Marketing - elective
• Data Mining - elective
• Statistics for Social Sciences - elective
• Statistics for Environmental Science - elective
• Engineering Statistics - elective

Course Program:

The course is structured as follows

The Instructor:

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 is the co-author with Dr. Michael Chernick of the forthcoming book An Introduction to Bootstrap Methods with Applications to R, and 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 Associate Professor of Statistics at Old Dominion University.

Organization of the Course:

The course takes place over the internet, at statistics.com. 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. The course is scheduled to take place over 3 weeks, and typically requires 15 hours per week. 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 and work through exercises. Discussion among participants is encouraged. The instructor will provide answers and comments.

Certificates and Grades:

You may be interested only in learning the material presented, and not be concerned with grades or certificates. Or you may be enrolled in a statistics.com Program in Advanced Statistical Studies that requires demonstration of proficiency in the subject, in which case your work will be assessed for purposes of issuing a grade. Or you may require only a "Certificate of Course Completion," along with professional development credit in the form of Continuing Education Units (CEU's). As you begin the class, you will be asked to specify your category.

Credit:

This course offers continuing education units (CEU's). For those successfully completing the course (generally this means marks of 50% or better on the homework), 2.5 CEU's and a certificate will be issued by statistics.com, upon request.

Dates:

Apr. 16 - May. 7, 2010
Aug. 13 - Sep. 3, 2010
Dec. 10, 2010 - Jan. 5, 2011
Click here to be notified of future course offerings.

Participants gain access to the online materials on the first day of the course, and typically spend about 15 hours per week (at their convenience). You retain full access to course materials, including discussion board, for two weeks after the course closing date.

Level:

Intermediate

Prerequisite:

You should have the equivalent of an introductory course in statistics such as Introduction to Statistics for Beginners, Introduction to Statistics 1: Inference for a Single Variable, and Introduction to Statistics 2: Working with Bivariate Data including a basic understanding of the concepts of statistical inference (confidence intervals and hypothesis tests). The math level is basic algebra. The additional preparation found in Introduction to Statistics 3: Regression and ANOVA is also helpful.

Course Text:

The required text is Matrix Algebra: An Introduction by Krishnan Namboodiri from Sage, which you can purchase here. 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). PLEASE ORDER YOUR COPY IN TIME FOR THE COURSE STARTING DATE. (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, and 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.

Registration:

Register Online - $399
Register Online (academic) - $299 (you must be affiliated with a college, university or high school)

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. Please use this printed registration form, for these and other special orders.

Note: 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.

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