We all know that calculus courses such as 18.01 and 18.02 are univariate and vector calculus, respectively. Modern applications such as machine learning and large-scale optimization require the next ...

ABSTRACT: In Kronecker products works, matrices are sometimes regarded as vectors and vectors are sometimes made in to matrices. To be precise about these reshaping we use the vector and diagonal ...

This is the course page for an 18.S096 Special Subject in Mathematics at MIT taught in January 2023 (IAP) by Professors Alan Edelman and Steven G. Johnson. For a previous version of this course, see ...

Impact Statement: We introduce a novel, closed-form GCN backpropagation solution, derived through matrix calculus, enabling precise and efficient training. The element-wise implementation directly ...

A manifestly Lorentz-covariant calculus based on two matrix-coordinates and their associated derivatives is introduced. It allows formulating relativistic field theories in any even-dimensional ...

Calculus, the mathematical study of continuous change, stands as a cornerstone of advanced mathematics and its applications. As you delve into this powerful branch of mathematics, you’ll discover a ...