Recent content by earlh

  1. E

    Prove a set is closed and bounded but not compact in metric space

    What is your definition of compact? The typical definition is every open cover has a finite subcover. Thus one way you could prove this is to find just one open cover such that there is no finite subcover.
  2. E

    Proof of Closed Sets: Cluster Points & Int. Pts

    A is closed if A^{C} is open is a perfectly reasonable definition, at least in topology, where the definition of open is the elements of the topology set. It's the standard definition, and it's used by Munkres which is the only text I have here.
  3. E

    Proof of Closed Sets: Cluster Points & Int. Pts

    And what's your definition of an open set?
  4. E

    Solve for q Value in F Distribution with Degrees of Freedom 1 & 2

    Do you actually have 3 degrees of freedom?
  5. E

    Solving Newton's Method for f(x) = 0: Step-by-Step

    Remember what \log(a/b) equals to? Break the pieces out.
  6. E

    Proof of Closed Sets: Cluster Points & Int. Pts

    Since everyone uses a slightly different definition of closed, can you post yours?
  7. E

    Proving the Identity Matrix Property: A^2=A for n-Rowed Matrices | 20 Marks

    Multiply A (I-A) and solve it. what does that tell you?
  8. E

    Finding SPD Matrix: Vanderberghe and Boyd Reader 6.4 Solution

    Symmetric positive definite -- sorry for using jargon
  9. E

    Proof of Eigenvector Property with Simple Linear Algebra

    Start like this: you know Ax = \lambda x and Bx = \lambda_{2} x from the definition of an eigenvector Thus Cx = (A + B)x = ... and go from there. I think it will be straightforward.
  10. E

    Finding SPD Matrix: Vanderberghe and Boyd Reader 6.4 Solution

    Hi -- so, I'm working through a text on my own 5 years out of college having completely forgotten more or less all linear algebra. Here's my problem -- 6.4 from a reader by Vanderberghe and Boyd which is btw excellent. Homework Equations I have to show when a matrix is SPD. Setup: let A...
  11. E

    Graduate Non-Zero Orthogonal Vectors: Show m<=n

    Dude, you already posted a thread like 2 days ago! https://www.physicsforums.com/showthread.php?t=306934
  12. E

    Graduate Suppose that{u1,u2, ,um} are non-zero pairwise orthogonal vectors

    Huh? If you want to say in words what you're having trouble expressing in a mathematical way, I'll help, but you need to put in the work to solve this. Think about the interaction between linear independence and orthogonality.
  13. E

    Graduate Suppose that{u1,u2, ,um} are non-zero pairwise orthogonal vectors

    I assume by dot you mean dot product / inner product? It helps if you are really clear about your notation -- eg is W a vector space, ring, module, etc. Second, in general, one fruitful way to start proofs like this is to take a simple example which you understand well and look at why your...