What is the meaning of $A. \\nabla - Mathematics Stack Exchange If $\mathbf A = \pmatrix{a_x\\a_y\\a_z}$, then $$(\mathbf A\cdot\nabla)\phi = a_x\frac{\partial}{\partial x}\phi + a_y\frac{\partial}{\partial y}\phi + a_z\frac{\partial}{\partial z}\phi$$ Basically, you treat $\nabla$ as a vector of derivatives and do vector algebra, except that you are careful not to move terms across the derivative
homework and exercises - Vector triple product with $\nabla$ operator . . . The vector calculus identity of the cross product of a curl holds: $$\mathbf{v} \times \left( \nabla \times \mathbf{a} \right) = \nabla_a \left( \mathbf{v} \cdot \mathbf{a} \right) - \mathbf{v} \cdot \nabla \mathbf{a} $$ where the Feynman subscript notation $\nabla_\mathbf{a}$ is used, which means the subscripted gradient operates only on the
matrices - Meaning of $\nabla \cdot \mathbf{A}$ for matrix $\mathbf{A . . . What is $\nabla \cdot \mathbf{A}$ when $\mathbf{A} \in \mathbb{R}^{m \times n}$ is a matrix, and where is there a consise definition of this notation? The Euler equations on Wikipedia contain terms on the form $\nabla \cdot (\mathbf{u} \otimes \mathbf{u} - w\mathbf{I})$ where $\mathbf{I}$ is the identity matrix Other material on the Euler
what does $(A\\cdot\\nabla)B$ mean? - Mathematics Stack Exchange Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
Proving $d^\\nabla( d^\\nabla \\omega) = F^\\nabla \\wedge \\omega$ What I said above answers your question But here are some extra good-to-know things In Riemannian geometry, it is often the case that people do not go higher than second derivatives, because ‘everything else is encoded in the curvature’