### Archive

Archive for August, 2012

## Differentiating Matrix Expressions The Easy Way, and an Elementary yet Genuine use for the Tensor Product

In many areas of science requiring differentiating multivariate functions $f: \mathbb{R}^n \rightarrow \mathbb{R}$, the derivative is often treated as a vector, and the second-order derivative treated as a matrix. This leads to notation with sometimes $\frac{df}{dx}$ appearing and sometimes its transpose $\left(\frac{df}{dx}\right)^T$ appearing. Extending this notation to higher derivatives, or to functions $f: \mathbb{R}^n \rightarrow \mathbb{R}^m$, becomes even more messy.