Akuna Capital Quant Researcher Interview Question
Matrix multiplication is a foundational operation in quantitative finance, machine learning, and scientific computing. However, as data sets continue to grow, efficiently multiplying large matrices becomes a significant challenge — especially in quantitative research roles such as those at Akuna Capital. In interviews for Quant Researcher positions, candidates are often asked to demonstrate their understanding of advanced matrix multiplication techniques, specifically when matrices are sparse or can be block-decomposed. In this article, we’ll delve into the theory, practical algorithms, and common interview strategies for efficient matrix multiplication using sparsity and block methods, providing a detailed answer to: How would you efficiently multiply two very large matrices using structures such as sparsity or block decomposition?
Matrix multiplication is defined as follows: Given two matrices \(A\) of size \(m \times n\) and \(B\) of size \(n \times p\), their product \(C\) is a matrix of size \(m \times p\), where the element at position \((i, j)\) is:
\[ C_{i, j} = \sum_{k=1}^{n} A_{i, k} \cdot B_{k, j} \]
