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The Vec-Permutation Matrix
Russell Akers
Abstract
Introduction
An Undergraduate Research Project is a great learning opportunity. For mathematics, it can also be a chance to see how concepts and results can be applied to actual problems. This project will be centered around the Vec-Permutation matrix and the vec operator. Learning how to use LaTEX will also be part of the Project.
Method
Definitions of the vec-permutation matrix and the vec operator can be used to prove many results. The vec operator takes partitioned columns of a matrix and stacks them successively. As part of the research, I will define the vec-permutation matrix and try to prove the results.
The Kronecker operator and Kronecker products will also be defined as part of the research.
Conclusion
I look forward to beginning my research and having some results to type up in LaTEX. I also hope to find applications of some of the results we will look at in the computer science field. This project will be a great opportunity for me to learn about aspects of mathematics that I have not been exposed to yet. I think it will be a great learning experience, as well as lots of fun.
Biography
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I am a senior in Mathematical Sciences at Montana Tech. As a child, and all through high school, I always loved mathematics. I came to Tech thinking that I might want to be an engineer, forgetting that for me, the best part of engineering is the math it employs. After switching majors, I discovered that linear algebra interests me. My research deals with matrices and some of their applications in statistics.
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