The Human Analysis Lab looks for people with strong very mathematical and programming skills to work on problems at the intersection of computer vision, machine learning, biometrics and computer graphics. If you think you may be interested, please get in touch with a solution to the following problem.

## Problem Description

Consider a matrix $A$ of size $\mathbb{R}^{nd\times nd}$, where each non-overlapping $d \times d$ block of the matrix, $D_{ij}$, is a diagonal matrix. So the matrix consists of $n^2$ such blocks. An example of such a matrix is shown below:

\begin{equation} \begin{bmatrix} D_{11} & D_{12} & D_{13} & \cdots & D_{1n} \\ D_{21} & D_{22} & D_{23} & \cdots & D_{2n} \\ \cdots & \cdots & \cdots & \cdots & \cdots \\ D_{n1} & D_{n2} & D_{n3} & \cdots & D_{nn} \end{bmatrix} \end{equation}

Construct an efficient data structure to represent such matrices and devise algorithms to perform matrix operations, such as matrix multiplications and matrix inverse, on the data structure you designed. Provide a technical write-up of your solution along with associated code implementing your solution.

## Ranking

MSU has strong research groups in AI, including Biometrics, Computer Vision, Pattern Recognition, Machine Learning, and NLP. If you use USNews rankings to guide your grad school search, please read this article.

As a transparent, accessible and informative ranking system, CSRankings is entirely based on the top-conference publications in each area of computer science. MSU is highly ranked in the computer vision area. When comparing United States schools between 2015 and 2020, or in the last two years, **MSU ranks No. 13, or No. 9** respectively.

## Graduate students

Graduate students from the CSE program of the Michigan State University can join the group. Masters students are also welcome. Graduate students are expected to have a strong mathematical background (linear algebra, probability and statistics, signal processing, information theory and real-analysis). Contact us with your resume, transcripts and the solution to the problem described above. Emails missing any of these will not be considered.

## Summer Interns

If you want to do an internship in the Human Analysis Lab, contact us at least 5 months in advance of your intended start date. Preference will be given to students who can intern for a longer period of time. Contact us with your resume, transcripts and the solution to the problem described above. Emails missing any of these will not be considered.

## Postdoctoral fellows

Please send (1) cover letter that includes the names and contacts for three references and a short statement of research interests, (2) a current CV and (3) code samples or links to published/distributed code to vishnu

@msu.edu.