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

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• Trying2Learn
In summary, dyadics are a construction used in linear algebra to represent a more complicated vector space.
Trying2Learn
TL;DR Summary
Hello!

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.

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.

Trying2Learn said:
Summary:: Simple discussion of a dyadic

Hello!

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.
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

## FAQ: What Is a Dyadic? - Understanding What They Are & How To Use Them

A dyadic is a mathematical concept that refers to a relationship or interaction between two objects or entities. It can also be described as a set of two elements that are related to each other in a specific way.

Dyadics are commonly used in physics and engineering to represent physical quantities that have both magnitude and direction, such as force or displacement. They are also used in social sciences to study relationships between individuals or groups.

## What are some examples of dyadics?

Some examples of dyadics include a force acting on an object, a magnetic field, and a communication channel between two people. In social sciences, a dyadic relationship can be seen between a parent and child, or between two friends.

## How are dyadics represented mathematically?

Dyadics are typically represented using matrices or tensors, which are arrays of numbers that describe the relationship between the two elements. The elements of the matrix or tensor correspond to the different components of the dyadic.

A dyadic involves two elements, while a monadic involves only one element. In other words, a dyadic relationship involves a pair or a set of two objects, while a monadic relationship involves a single object or entity.

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