possible research topic for linear algebra

I am an undergraduate student. I have to do a research project for my homework assignment. This is my first maths research so I have no idea what topic should I select and how to start....

I want to do a research which related to **Linear algebra** because i have just completed this course. Can anyone suggest me the possible and interesting research topics in linear algebra?

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Below is the guideline of the research areas which given by my professor:

The areas of research must be mathematics and its applications, such as:

- Basic research: algebra, analysis, geometry, probability, statistics, etc.
- Engineering applications: computing, internet, communications, information and digital technology, etc.
- Commercial applications: economics, finance, logistics, management, decision science, operations research, transportation, etc.
- Scientific applications: medicine, physics, chemistry, biology, environment and health problems, etc.
- Innovation designs: image and visualization, games, puzzles, algorithms, etc.

Thank you very much !