projections

[hardy hound]

where do i start from for this question?

[steady turtle]

1. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
2. Wait patiently for a helper to come along.
3. Once someone helps you, say thank you and close the thread with:

   +close
   

4. Feel free to nominate the person for helper of the week in #helper-nominations
5. Do not ping the mods, unless someone is breaking the rules.
6. If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[undone pine]

Recall that the projection of b onto a is proj(a, b) = ((a·b)/(b·b))b. And the orthogonal projection is then b - proj(a, b).

Just remember that the inner product isn't standard.

[hardy hound]

got confused by the defition of the inner product

got it thanks!

[undone pine]

You're welcome!
If you're not sure how that is an inner product, consider this.

[hardy hound]

inner product is basically a function which follows certain conditions?

the video said id have to prove few statemetns to show that this is an inner product

[elder badge]

You do, indeed

Seeing that the square matrix is symmetric, your newly defined bilinear form is certainly symmetric

But is it positive?

Gotta get those eigenvalues

[undone pine]

Yup. In general, any inner product of two vectors in ℝ^n can be represented as u·v = u^T A v, where A is a symmetric positive definite matrix.

[hardy hound]

yupp we got its know its bilinear and we can prove this too ig

[hardy hound]

got it thanks

[sweet finch]

@hardy hound has given 1 rep to @undone pine