Matrix Algebra Review

taught by Robert LaBudde

Brief Description:

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.

Instructor(s):
Level: Intermediate

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.

Dates:
June 29, 2012 to July 27, 2012November 02, 2012 to November 30, 2012
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Registration:
Please read the syllabus tab, noting the prerequisites, text and software requirements.

Register Online -$499
Register Online -$399 (you must be affiliated with a college, university or high school)

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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. Multiple course registrations may be entitled to tuition discounts; read more.

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Matrix Algebra Review

taught by 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.

Prerequisite(s):

If you are unclear as to whether you have mastered the requirements, try these placement tests here.

The math level is basic algebra. The additional preparation found in Introduction to Statistics 3: Regression and ANOVA is also helpful.

 

Course Program:

SESSION 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

SESSION 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

SESSION 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

SESSION 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

HOMEWORK:

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

Organization of the Course:

This course takes place over the internet 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.

The course 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, 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.

Credit:
Students come to the Institute for a variety of reasons. As you begin the course, you will be asked to specify your category:

1. You may be interested only in learning the material presented, and not be concerned with grades or a record of completion.
2. You may be enrolled in PASS (Programs in Analytics and Statistical Studies) that requires demonstration of proficiency in the subject, in which case your work will be assessed for a grade.
3. You may require a "Record of Course Completion," along with professional development credit in the form of Continuing Education Units (CEU's).  For those successfully completing the course, 5.0 CEU's and a record of course completion will be issued by The Institute, upon request.

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.

Register Now

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Matrix Algebra Review

taught by Robert LaBudde

Instructor(s):
Dates:
June 29, 2012 to July 27, 2012November 02, 2012 to November 30, 2012
Course Fee: $499
Academic Rate: $399

Before registering, please read the syllabus tab, noting the prerequisites, text and software requirements. When you click the register button, you will be taken to our secure transaction page.

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