# Matrix Algebra Review

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 414 STAT 501 STAT 504 STAT 505 1.0 - Matrix Definitions Required Required Required Required 2.0 - Matrix Arithmetic Required Required Required Required 3.0 - Matrix Properties Required Required Required Required 4.0 - Matrix Inverse Required Required Required Required 5.0 - Advanced Topics Recommended Recommended Recommended 5.1, 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.