Recent content by PhillipKP

  1. P

    Graduate Understanding the weak norm and it's notation

    Thank you! That was nice and quick!
  2. P

    Graduate Understanding the weak norm and it's notation

    Hello. I'm trying to grasp the notation for the definition of something called the weak q-norm, defined as \|x\|_{q,w}^q = \sup\limits_{\epsilon > 0} \epsilon^q \left| \Big\{i \,|\, |x_i| > \epsilon \Big\} \right| I don't come from a pure math background so I've never seen this...
  3. P

    Physics Physicists' Time: Do They Have Enough?

    It really depends on your boss/company like any job.
  4. P

    Undergrad What's the difference between a dictionary and a basis?

    No worries. :)
  5. P

    Undergrad What's the difference between a dictionary and a basis?

    It's used in signal processing and specifically in the new field of compressive sensing. This is where I first encountered it: http://www-stat.stanford.edu/~candes/papers/CoherentCS.pdf
  6. P

    Undergrad What's the difference between a dictionary and a basis?

    I see the term dictionary used a lot and it sounds a lot like a basis for a vector space. But what is the different? Can we collection of vectors be both a basis and a dictionary? Thanks
  7. P

    Optics: Find the index of refraction

    There is a relationship between the index, optical path length, and phase. The higher the index, the more the optical path length, and the more the phase delay a light will have as it traverses a piece of glass. The point of a converging (aka positive aka convex) lens is to induce more...
  8. P

    Trying to prove F^infinity is infinite dimensional

    Never mind this was due last week and my proof was correct according to the solutions.
  9. P

    Trying to prove F^infinity is infinite dimensional

    I don't understand where you are trying to go with this. There is no contradiction if you suppose that it is not infinite dimensional.
  10. P

    Trying to prove F^infinity is infinite dimensional

    It's not in the list \beta, it's in the span of \beta. Right?
  11. P

    Trying to prove F^infinity is infinite dimensional

    Homework Statement Theorem: Prove that \mathbb{F}^{\infty} infinite dimensionalHomework Equations Definition of Infinite Dimensional Vector Space: A vector space that is not finite dimension Definition of Finite Dimensional Vector Space: \exists list of vectors in it that spans the space...
  12. P

    Prove the sum of two subspaces is also a subspace.

    OK I think I got it. Thanks guys!
  13. P

    Prove the sum of two subspaces is also a subspace.

    Ok thank you. Let me think about this some and try to make some progress. I'll be back later in the day.
  14. P

    Prove the sum of two subspaces is also a subspace.

    Homework Statement Hi I'm trying to prove that the sum of two subspaces U and W is also a subspace. Homework Equations U is a subspace of V if U is also a vector space and it contains the additive identity, is closed under addition, and closed under scalar multiplication. The definition of...
  15. P

    Solve Summation Confusion: Homework Equations & Attempted Solution

    That was perfect thanks :)