What is Vector Inversion and How Does It Differ from Vector Division?

[jasper353]

How do you get a vector to the power of negative one?

I.E. : V ^ (-1)?

Or inversion if that's what it's called?

Thank you.

 

[HallsofIvy]

I have never seen "division", or for that matter powers or products defined for vectors. Perhaps if you told us where you saw that and the situtation involved, we could say.

In edit: It has been pointed out to me that I forgot the "cross product" of vectors- but that is only defined for three dimensional vectors and still does not have multiplicative inverses defined.

 

[Ed Aboud]

https://www.physicsforums.com/showthread.php?t=226881

May be of help jasper...

 

[jasper353]

I see that it is more involved than I was hoping.

I followed the thread, and the other person is,

or was, having the same difficulty as I am or were.

Thanks :). Jasper.

 

[CellCoree]

I would like to clarify that vector division and inversion are two different mathematical operations. Vector division involves dividing one vector by another, resulting in a new vector. On the other hand, vector inversion refers to the process of finding the inverse of a vector, which is a vector that, when multiplied by the original vector, results in the identity vector (a vector with all components equal to 1).

To get a vector to the power of negative one, you can use the concept of vector inversion. This means finding the inverse of the vector and raising it to the power of one, which is equivalent to taking the reciprocal of each component of the vector. For example, if we have a vector V = (2,4), the inverse of this vector is V^-1 = (1/2, 1/4). Therefore, V^(-1) = (1/2)^1, (1/4)^1 = (1/2, 1/4).

It is important to note that vector inversion is only defined for non-zero vectors. Additionally, vector inversion is a mathematical concept and may not have a physical meaning in certain scientific fields. It is always necessary to understand the context and application of vector operations in a scientific scenario.