What Does Skew Symmetry Imply for One-Dimensional Systems?

In summary, the original equation given is p_dot = S(omega)*p, where p = [x, y, z] is the original states, omega = [p, q, r] and S - skew symmetric. The question is asked how the equation would appear if only the state z is considered. It is unclear what skew symmetry would mean in one dimension and it is irrelevant in the context of the question, which may be related to quantum physics.
  • #1
hoddy
4
0
TL;DR Summary
if I have a equation like (just a random eq.) p_dot = S(omega)*p. where p = [x, y, z] is the original states, omega = [p, q, r] and S - skew symmetric. How does the equation appear if i only want a system to have the state z?
Hi,

if I have a equation like (just a random eq.) p_dot = S(omega)*p. where p = [x, y, z] is the original states, omega = [p, q, r] and S - skew symmetric.
How does the equation appear if i only want a system to have the state z? do I get z_dot = -q*x + p*y. Or is the symmetric not valid so I simply get z_dot = z? or something else?
and the same for rotation matrix? : p_dot = R(omega)*p

Thanks for any replies!
 
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  • #2
hoddy said:
(just a random eq.)
You are asking us to decode a random equation that you made up?

And it would help if you would please learn to post math equations using LaTeX. That would make your postings a lot more clear (well, maybe not if you keep posting random equations...).

The PF LaTeX tutorial is available in the Help pages, under INFO at the top of the page.
 
  • #3
Hi berkeman. sorry, here is the complete equation with v, omega, f and g beeing 3x1 vectors:
awd.PNG


Im just curious about the first term with the skew symmetric, how it will turn out when I only have it in 1 dimension, like described in original post.
 
  • #4
What should skew symmetry mean in one dimension? S=0? I suspect from your question that we speak about quantum physics, and the three dimensional skew symmetric matrices form a semisimple Lie algebra. It's no longer semisimple in the one dimensional case which is crucial, skew symmetric or not, hence irrelevant in the context you hinted at.
 

Related to What Does Skew Symmetry Imply for One-Dimensional Systems?

1. What is a skew symmetric 1 dimension?

A skew symmetric 1 dimension is a mathematical concept that describes a matrix or vector that is equal to its negative transpose. In simpler terms, it is a one-dimensional array of numbers that when flipped and multiplied by -1, remains unchanged.

2. How is skew symmetry different from symmetry?

Skew symmetry and symmetry are two different mathematical concepts. Symmetry refers to an object or pattern that has a balance or mirror image on both sides. Skew symmetry, on the other hand, refers to a mathematical property of matrices or vectors that are equal to their negative transpose.

3. What are the properties of a skew symmetric 1 dimension?

The main property of a skew symmetric 1 dimension is that it is equal to its negative transpose. This means that if you flip the matrix or vector and multiply it by -1, it will remain unchanged. Another property is that the main diagonal of a skew symmetric matrix or vector is always zero.

4. How is skew symmetric 1 dimension used in real life?

Skew symmetric 1 dimension is used in various fields, including physics, engineering, and computer science. In physics, it is used to describe the properties of angular momentum and magnetic fields. In engineering, it is used to solve problems related to rotational motion and vibrations. In computer science, it is used in algorithms for image and signal processing.

5. Can a skew symmetric 1 dimension have more than one dimension?

No, a skew symmetric 1 dimension, by definition, only has one dimension. This means that it is a one-dimensional array of numbers that satisfies the properties of skew symmetry. If a matrix or vector has more than one dimension and still satisfies the property of skew symmetry, it would be classified as a skew symmetric multi-dimensional array.

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