# What is a dyadic?

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.

## Answers and Replies

anuttarasammyak
Gold Member
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
Mentor
2021 Award
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.

Thank you, everyone

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