Flucky said:Homework Statement
I need to find Λ using the equation below (I think).
Homework Equations
A [/B]+ ∇Λ = 0
where A(x,y,z,t) = B[itex]\begin{pmatrix} x+y\\ x-y\\ 0 \end{pmatrix}[/itex]
The Attempt at a Solution
Is this at all possible?
stevendaryl said:I'm not sure about your notation, is [itex]A[/itex] a matrix, or a vector? Do the three components [itex]x+y, x-y, 0[/itex] correspond to vector components, or matrix components?
stevendaryl said:I'm not sure about your notation, is [itex]A[/itex] a matrix, or a vector? Do the three components [itex]x+y, x-y, 0[/itex] correspond to vector components, or matrix components?
stevendaryl said:Assuming that you mean that [itex]A[/itex] is a vector, then your problem is to find a function [itex]\Lambda(x,y,z)[/itex] such that
[itex]\nabla \Lambda = -A = -B(x+y, x-y, 0)[/itex]
That means that there are three equations for [itex]\Lambda[/itex]:
- [itex] \frac{\partial}{\partial x} \Lambda = -B (x + y)[/itex]
- [itex]\frac{\partial}{\partial y} \Lambda = -B (x - y)[/itex]
- [itex]\frac{\partial}{\partial z} \Lambda = 0[/itex]
stevendaryl said:Assuming that you mean that [itex]A[/itex] is a vector, then your problem is to find a function [itex]\Lambda(x,y,z)[/itex] such that
[itex]\nabla \Lambda = -A = -B(x+y, x-y, 0)[/itex]
That means that there are three equations for [itex]\Lambda[/itex]:
- [itex] \frac{\partial}{\partial x} \Lambda = -B (x + y)[/itex]
- [itex]\frac{\partial}{\partial y} \Lambda = -B (x - y)[/itex]
- [itex]\frac{\partial}{\partial z} \Lambda = 0[/itex]
You should always include the full problem as well as your attempts to solve it.Flucky said:Hmm I think I may have to post the question in full. My original post is just a small part of a bigger question (about Gauge transformations) so I am probably going about it wrong.
A gradient with vector is a mathematical concept used to describe the direction and magnitude of change in a vector field. It is represented by a vector that points in the direction of the steepest increase of a function at a specific point.
To find the gradient with vector, you first need to calculate the partial derivatives of the function with respect to each variable. These partial derivatives are then combined to form a vector, which represents the direction and magnitude of the gradient at a specific point.
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