![]() ![]() Note that I have assumed the eulicdean basis (i. ![]() The gradient of a vector field corresponds to finding a matrix (or a dyadic product) which controls how the vector field changes as we move from point to another in the input plane.ĭetails: Let $ \vec$Īnd that's what the gradient of a vector field is, a big matrix controls how the gradient vector changes when we move in any direction of the input space. So to answer your question, the gradient of a vector field is the sum of a scalar field and a bivector field. So $\nabla \wedge \vec v$ is called a bivector field. In the same way that a vector field can be though of as associating with every point in your domain an oriented line segment (a vector), $\nabla \wedge \vec v$ associates with every point in your domain an oriented plane segment (which we call bivectors). However the second term is a different type of object entirely (actually, it's a generalization of the familiar $3$D curl $\nabla \times \vec u$ that works in any dimension). The first term should be familiar to you - it's just the regular old divergence. So we get $\nabla\vec v = \nabla \cdot \vec v \nabla \wedge \vec v$. A vector field is a specific type of multivector field, so this same formula works for $\vec v(x,y,z)$ as well. Here is how the Potential gradient through potentiometer calculation can be explained with given input values -> 0.25 (18-17)/4. In geometric calculus, we have the identity $\nabla A = \nabla \cdot A \nabla \wedge A$, where $A$ is a multivector field. To use this online calculator for Potential gradient through potentiometer, enter Electric Potential Difference (V), Electric Potential Diff through other Terminal (V B)
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