Finding the inner product formulla

In summary, the conversation is about finding the formula for the inner product that defines a certain norm. The speaker is trying to solve a problem involving a vector and a subspace, and needs the inner product formula to find the minimal difference between the original vector and its projection onto the subspace. The speaker is asking if there is a general method for finding this formula, as they have been unable to guess it in this particular case.
  • #1
lom
29
0
once i solve that one is the derivative of the other
but here its much harder to guess the formulla
http://i47.tinypic.com/ixt74i.jpg
what is the general method?
 
Last edited:
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  • #3
i want to find the formula for the inner product which defines such norm.


?
 
  • #5
You still haven't told us what the entire problem is- that looks like part of a problem. Three numbers don't "define" anything!
 
  • #6
i need to find alpha beta and gama
so this expression will be minimal

i know how to solve such stuff
usually
i have a vector and a subspace to make a projection of the vector

so i make an orthogonal basis and then i make a projection of that vector
into my space

and then the difference between that vector and the original vector is the minimal

but in order to do all that i need the
inner product formula which defines this norm.

usually i figured out the formula by guessing

but here i can't guess

so i am asking if there is a general method
?
 

1. What is the inner product formula?

The inner product formula is a mathematical tool used to calculate the dot product of two vectors in a vector space. It is used to measure the angle between two vectors and is an important concept in linear algebra and vector calculus.

2. How is the inner product formula calculated?

The inner product formula is calculated by taking the sum of the products of the corresponding components of two vectors. This can also be represented as the first vector multiplied by the transpose of the second vector.

3. What is the significance of the inner product formula in mathematics?

The inner product formula is significant because it allows us to measure the similarity between two vectors and can be used to define important mathematical concepts such as orthogonality and projection.

4. Can the inner product formula be extended to other mathematical structures?

Yes, the inner product formula can be extended to other mathematical structures such as matrices and functions. However, the definition and calculation may differ slightly depending on the structure being used.

5. How is the inner product formula used in real-life applications?

The inner product formula has many applications in various fields such as physics, engineering, and computer science. It is used in signal processing, image recognition, and machine learning algorithms to name a few. It also has applications in calculating work done by a force, finding the angle between two lines, and measuring the closeness of two data points in statistical analysis.

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