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 Statistics.com. For more details please visit at http://www.statistics.com/matrixalgebra/.**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 statistics.com 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 statistics.com accepts registration for its courses at special
prices in Indian Rupees through its partner, the Center for eLearning and
Training (C-eLT), Pune.

Call: 020 66009116

Websites:

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