Thursday, 11 October 2012

Matrix Algebra Review

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. Learn with Dr. Robert LaBudde in his online course "Matrix Algebra Review" at For more details please visit at

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.

Course Program:

Course outline: The course is structured as follows

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, orthogonally

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

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 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.

You will be able to ask questions and exchange comments with Dr. Robert LaBudde via a private discussion board throughout the course.   The courses take place online at in a series of 4 weekly lessons and assignments, and require about 15 hours/week.  Participate at your own convenience; there are no set times when you must be online. You have the flexibility to work a bit every day, if that is your preference, or concentrate your work in just a couple of days.

For Indian participants accepts registration for its courses at special prices in Indian Rupees through its partner, the Center for eLearning and Training (C-eLT), Pune.

For India Registration and pricing, please visit us at

Call: 020 66009116


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