Carmen's Graphics Blog
What are the differences between the Jacobian, the Hessian and the Gradient? All three have ties to multivariable calculus, let's dive in and take a look!
When studying multivariable calculus, we often come across the use of matrices to represent different concepts. We often come across the Jacobian, the Hessian and the gradient.
These concepts are close to each other, by virtue of being matrices having to do with derivatives of functions, However, each matrix has its own derivation, and signification.
What is the difference between the Jacobian, the Hessian and the gradient 🤔? We will discover it together in this article. During this mathematical journey, we will also study the concepts of the difference between vector-valued functions and scalar-valued functions.
We start with the gradient which we already talked about a few weeks ago. The gradient is a vector composed of the partial derivatives of a scalar-valued function, ff f :
