Tagged Questions
1
vote
1answer
302 views
Bra space and adjoint vectors
If I'm not wrong, a bra, $ \langle \phi_n | $, can be thought as a linear functional that when applied to a ket vector, $| \phi_m \rangle$, returns a complex number; that is, the inner product it's a ...
5
votes
6answers
2k views
How is gradient the maximum rate of change of a function?
Recently I read a book which described about gradient. It says
$${\rm d}T~=~ \nabla T \cdot {\rm d}{\bf r},$$
and suddenly they concluded that $\nabla T$ is the maximum rate of change of $f(T)$ ...
1
vote
2answers
392 views
What is the physical meaning of a product of vectors?
My teacher told me that Vectors are quantities that behave like Displacements. Seen this way, the triangle law of vector addition simply means that to reach point C from point A, going from A to B ...
9
votes
4answers
3k views
How can area be a vector?
My professor told me recently that Area is a vector. A Google search gave me the following definition for a vector:
Noun: A quantity having direction as well as magnitude, esp. as
determining ...
4
votes
1answer
1k views
Uniqueness of Helmholtz decomposition?
Helmholtz theorem states that given a smooth vector field $\pmb{H}$, there are a scalar field $\phi$ and a vector field $\pmb{G}$ such that
$$\pmb{H}=\pmb{\nabla} \phi +\pmb{\nabla} \times \pmb{G},$$
...
1
vote
3answers
906 views
Can vectors in physics be represented by complex numbers and can they be divided? [closed]
Below is attached for reference, but the question is simply about whether vectors used in physics in a vector space can be represented by complex numbers and whether they can be divided.
In ...
