Looking for a question in orthogonality

In summary, orthogonality refers to the property of two or more objects being perpendicular or at a right angle to each other. It is determined using methods such as the Pythagorean theorem or the dot product. Orthogonality is important in science as it simplifies complex systems and allows for easier calculations. It can exist in any number of dimensions and is used in data analysis for reducing dimensionality and identifying relationships between variables.
  • #1
transgalactic
1,395
0
i know that there could be the use of integrals in orthogonal things

??
 
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  • #2
Erm... perhaps you should elaborate...
 
  • #3
the use of integrals in orthogonality
question about that
maybe polinomials vectors
i need a question that asks about such stuff
??
 
  • #4
It depends on how the inner product for a particular inner product space is defined. An inner product can be defined in several different ways, one of which is as a definite integral.
 
  • #5
yes like this one
do you have an example?
 
  • #7
yyes
 

FAQ: Looking for a question in orthogonality

What is orthogonality?

Orthogonality, in the context of mathematics and science, refers to the property of two or more objects being perpendicular or at a right angle to each other. In linear algebra, it also refers to the property of two vectors being independent or at a 90-degree angle to each other.

How do you determine orthogonality?

To determine orthogonality, you can use various methods depending on the context. In geometry, you can use the Pythagorean theorem to calculate the length of sides and determine if they are perpendicular. In linear algebra, you can use the dot product to determine if two vectors are at a right angle to each other.

What is the importance of orthogonality in science?

Orthogonality is important in science because it allows us to simplify complex systems and make calculations easier. In physics, for example, orthogonal vectors can represent independent forces acting on an object. In engineering, orthogonal projections can be used to calculate the relationship between different variables in a system.

Can orthogonality exist in more than two dimensions?

Yes, orthogonality can exist in any number of dimensions. In three-dimensional space, for example, three vectors can be orthogonal to each other if they form a right angle. In higher dimensions, orthogonality can be defined using the dot product or other methods.

How is orthogonality used in data analysis?

In data analysis, orthogonality is used to reduce the dimensionality of data and identify relationships between variables. In principal component analysis, for example, orthogonal components are created to represent the most variation in a dataset. In regression analysis, orthogonal functions can be used to model the relationship between variables.

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