Hey folks! I ran into this notation while reading Chapter 8.4 of Evans' Partial Differential Equations—it's page 471 in the printed book, and page 474 in the PDF copy. Just to set the context: here we have functions $u, v: \mathbf{R}^n \to \mathbf{R}^m$, and $D\mathbf{u}$ is defined as the Jacobian matrix of $\mathbf{u}$.

I'm confused about what $D\mathbf{u} : D\mathbf{v}$ stands for. From how it's used, it looks like this should be a scalar-valued function, so I'm guessing the colon : might be the Hadamard product (element-wise multiplication) of the two matrices? But I want to make sure I'm not misinterpreting it.

Any insights would be super appreciated—thanks a ton in advance!

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