ronm

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About ronm

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  1. A question on matrix calculation

    any suggestion pls? Thanks,
  2. A question on matrix calculation

    Thanks for your comment. Basically I want to have a Statistical test as H0: A * Sigma * A' = B * Sigma * B' Here the only population parameter is Sigma, which can be estimated from sample observations. Therefore I know the distribution of Sigma_Sample. And from this I can derive the distribution of C * Sigma * C'. Therefore if can somehow write (A * Sigma * A') - (B * Sigma * B') = C * Sigma * C' then I can construct a Test Statistic for my testing. Please let me know if you need more information. It will also be very helpful if you can propose some better alternative of my testing problem. Thanks and regards,
  3. A question on matrix calculation

    okay, let say r = 1 and n > 1. In this restricted scenario what will be the case? Thanks,
  4. Hello all, let say I have a PD symmetric matrix Sigma (order n) and two matrices A and B as order rXn. Now consider the expression: (A * Sigma * A') - (B * Sigma * B') Can I write this expression as (C * Sigma * C')? Thanks for your help.
  5. Hi all, I have a probably simple question on a general function, let say I have a real valued function y = f(x), x >= 0 Now I have calculated that for all x, the 1st derivative is always negative and the 2nd derivative is always positive. With this finding, can I infer that, the 1st derivative will always decrease (in absolute value) as I move onward in x? Thanks for your comment. Thanks and regards,
  6. Comparing VCV matrices

    Thanks all for your replies. My goal is to quantify the difference between 2 given VCV matrices. Here, I can take those VCV matrices for 2 multivariate normal distributions (with same location parameter.) Therefore I think KL divergence metric should be okay for now. Let see and discuss this with my colleagues. One more question. That metric will essentially give some number (whatever it is.) However is there any criterion or general practice to say: whether that number is big or small? How much should I tolerate? I appreciate your suggestion. Thanks,
  7. Hi there, I need to compare two Variance-covariance matrices for 2 arbitrary random vectors (assuming both are multivariate normal with Zero location). I am aware of different Matrix norms and primarily thought of using some of them to compare 2 matrices. However I was wondering what is the best metric to compare specifically VCV matrices as, VCV matrix can not be any arbitrary general matrix therefore there may be some special treatment for this purpose? My goal is to ***properly capture*** the difference between 2 VCV matrices. Can somebody guide me? Thanks,
  8. Dear all, suppose I have 3 positive numbers in order N1 < N2 < N3. Then can I say that, this inequality will always hold: (N1 + N3) > 2*(N2). Thanks for your time.
  9. An inequality

    My god.........so easy? Thanks so much Alvaro
  10. An inequality

    I really cant understand what is going on here? Why you have written [color=#1C2837][size=2](1-0.1)[sup]2[/sup][/size][/color]? I have expression (1 - 0.1^2)/(1 - 0.1) < 2 (this I need to prove algebraically). Even Nanoha wrote at 1st place "[color=#1C2837][size=2](1-a^n) <= 1 - a[/size][/color]". "n" must be within bracket right?
  11. An inequality

    are you sure that [color=#1C2837][size=2](1-a^n) <= 1 - a? a is within (0, 1)[/size][/color]
  12. An inequality

    Oops there is a typo: it should be [color=#1C2837][size=2](1 - a^n)/(1 - a) < n[/size][/color] [color=#1C2837][size=2] [/size][/color] [color=#1C2837][size=2]Any view?[/size][/color]
  13. An inequality

    Dear all, suppose "a" is positive number less than 1 and "n" is a positive integer greater than 1. Does the below inequality always hold? ((1 - a)^n)/(1 - a) < n I have run few simulations and found that above inequality always hold. But is this possible to see it analytically, what is going on inside? Thanks,
  14. Dear all, let say I have a real matrix (non-null) A and A^t, t is a positive integer, tends to zero as t tends to infinity. Given this information can I infer that, all eigen values of this matrix will be less than 1 in absolute term? Any online reference will be highly appreciated. Thanks for your time.