Thank you so much for posting. I finally understand Jacobian matrix. The key is to know this applies to a function that returns multiple values. The wikipedia article was difficult to understand, until now! Note: Technically, a function can map an input to a single output only. Here, when we say a function returns multiple values, we mean a single set of multiple values. For example, a function that outputs the heating and cooling cost of a building. Where as, a circle is not a function because it outputs two y values for a single x.