Matrix Algebra Review

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:
February 24, 2012 to March 23, 2012June 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.

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Matrix Algebra Review

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):
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 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

Organization of the Course:

This course takes place over the internet, at statistics.com 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 you will receive individual feedback on your homework answers.

Credit:
Students come to The Institute for a variety of reasons:

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 (Program in Advanced 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).

As you begin the class, you will be asked to specify your category.

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), 5.0 CEU's and a record of course completion will be issued by Statistics.com, 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.

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Matrix Algebra Review

Instructor(s):
Dates:
February 24, 2012 to March 23, 2012June 29, 2012 to July 27, 2012November 02, 2012 to November 30, 2012
Course Fee: $499
Academic Discounted 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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