Undergrad What Is a Dyadic? - Understanding What They Are & How To Use Them

[Trying2Learn]

TL;DR

Simple discussion of a dyadic

Hello!

I have always had difficulty understanding dyadics.

The operation of two vectors, side by side, just seems weird.

I finally went to wikipedia and found this sentence:
A dyadic can be used to contain physical or geometric information, although in general there is no direct way of geometrically interpreting it.

So, with that, could someone explain what a dyadic is? Is is really just a juxataposition of two vectors to "organize" information? Is that all?

I am embarrased to say that I just do not see an "operation" here. I do not see what use they have.

 

[anuttarasammyak]

I think it is tensor written as
a^i b^j:=c^{ij}
where $a^i$ and $b^j$ are vectors.

Sum of these numbers such as antisymmetric tensor
a^i b^j-a^j b^i
symmetic tensor
a^i b^j+a^j b^i
are also tensors.

 

[fresh_42]

Summary:: Simple discussion of a dyadic

Hello!

I have always had difficulty understanding dyadics.

The operation of two vectors, side by side, just seems weird.

I finally went to wikipedia and found this sentence:
A dyadic can be used to contain physical or geometric information, although in general there is no direct way of geometrically interpreting it.

So, with that, could someone explain what a dyadic is? Is is really just a juxataposition of two vectors to "organize" information? Is that all?

I am embarrased to say that I just do not see an "operation" here. I do not see what use they have.

Have a read:
https://www.physicsforums.com/insights/what-is-a-tensor/

A dyadic is $v\otimes w$. They are bilinear and span a vector space. If you introduce coordinates, then you get a matrix. A matrix of rank $1$. The operation, in this case, is matrix multiplication, namely column $(n,1)$ times row $(1,m).$ This is the technical construction. And like any matrix, we can interpret it as a linear function and start with linear algebra. When physicists speak of tensors, they only mean more complicated vector spaces like tangent bundles.

 

[Trying2Learn]

Thank you, everyone

I forgot about this question (was intending to ask another), but this great. Thank you.