Matrix Algebra Review

Printer-friendly versionPrinter-friendly version
matrix transpose

The transpose of a matrix can be obtained by reflecting the elements along the main diagonal. Transposing twice returns the matrix to the original form. (Public Domain)

Matrix Algebra: A Review

The Prerequisites Checklist page on the Department of Statistics website lists a number of courses that require a working knowledge of Matrix algebra as a prerequisite.  Students who do not have this foundation or have not reviewed this material within the past couple of years will struggle with the concepts and methods that build on this foundation.  The courses that require this foundation include:

STAT 414 - Introduction to Probability Theory
STAT 501 - Regression Methods
STAT 504 - Analysis of Discrete Data
STAT 505 - Applied Multivariate Statistical Analysis

Review Materials

Many of our returning, working professional students report that they had taken courses that included Matrix algebra topics but often these courses were taken a number of years ago.  As a means of helping students assess whether or not what they currently know and can do will meet the expectations of instructors in the courses above, the online program has put together a brief review of these concepts and methods.  This is then followed by a short self-assessment exam that will help give you an idea if you still have the necessary background.

Self-Assessment Procedure

1. Review the concepts and methods on the pages in this section of this website.   Note the courses that certain sections are aligned with as prerequisites:

 STAT 414STAT 501STAT 504STAT 505
1.0 - Matrix Definitions Required Required RequiredRequired
2.0 - Matrix Arithmetic Required Required RequiredRequired
3.0 - Matrix Properties Required Required RequiredRequired
4.0 - Matrix Inverse Required Required RequiredRequired
5.0 - Advanced Topics Recommended Recommended Recommended5.1, 5.4, Required
5.2, 5.3, Recommended

2.  Download and complete the Self-Assessment Exam

3.  Review the Self-Assessment Exam Solutions and determine your score.

Students who score below 70% (fewer than 21 questions correct) should consider further review of these materials and are strongly encouraged to take a course like MATH 220 (Penn State course description) or an equivalent course at a local college or community college.

If you have struggled with the concepts and methods that are presented here, you will indeed struggle in the courses above that expect this foundation.

Please Note:  These materials are NOT intended to be a complete treatment of the ideas and methods used in Matrix algebra. These materials and the self-assessment are simply intended as simply an 'early warning signal' for students.  Also, please note that completing the self-assessment successfully does not automatically ensure success in any of the courses that use these foundation materials.