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  1. perplexabot

    12VDC/2A power adapter to power two systems?

    Thank you for the quick reply! Great to hear it is that simple! Unfortunately now I have to solder together a new circuit for the TO3 instead of using an older circuit i had with the TO220. Oh well, shouldn't be too bad. Thanks again. EDIT: DAMN! Those TO3's are 40 bucks on digikey!
  2. perplexabot

    12VDC/2A power adapter to power two systems?

    Hey! So I have a raspberry pi that uses 5V/1.2A and a LCD monitor that uses 12v/0.2A. I would like to power both using a single wall power outlet. I found a power adapter that converts 100-240VAC/50-60Hz/1.2A to 12VDC/2A. I was wondering if it is as easy as cutting off the connector on the...
  3. perplexabot

    MATLAB Solve Riccati (DARE) with MATLAB

    I have run my code. I got an answer but I am confused with the result as it is not as I expected. I am trying to figure out why the answer is what it is. I was wondering whether my DARE formulation was correct (hence, why I have this post).
  4. perplexabot

    MATLAB Solve Riccati (DARE) with MATLAB

    No problem! I still appreciate the fact that you are trying to help. Thank you.
  5. perplexabot

    MATLAB Solve Riccati (DARE) with MATLAB

    That's the same link I provided in my original post : (
  6. perplexabot

    Software for multiplication of matrices

    Matlab is capable of doing symbolic matrix multiplication, and is actually really simple (just trying to expel any fears of the OP). MATLAB is an option for symbolic multiplication.
  7. perplexabot

    MATLAB Solve Riccati (DARE) with MATLAB

    Hey all, I was wondering if you can help me define the arguments for the dare() function of matlab. Here is the DARE form I have: \begin{equation} \begin{split} \Phi(p_\infty) &= \Phi_\infty = \Phi_{33}-\Phi_{32}(\Phi_\infty+\Phi_{R})^{-1}\Phi_{23}\\...
  8. perplexabot

    A Derivative of log of normal distribution

    Thank you very much. I will continue to read on probability spaces and touch up up sigma algebra. I am really thankful for your time and help. Thank you for offering more help on this topic (I will take you up on your offer : p).
  9. perplexabot

    B Why can you choose only V in DC but V and I in AC?

    All I said was the transformer isolates the input supply from the circuit in question thus the impedance of the circuit connected to the secondary is NOT typically seen at the primary. Is that a wrong statement?
  10. perplexabot

    B Why can you choose only V in DC but V and I in AC?

    The transformer that is used for connecting an AC power supply isolates the supply from the circuit in question, thus the ac supply will not "see" the resistance of the circuit, only the impedance of the primary coil of the transformer (to some extent). Yes, DC is AC as f->0 but the transformer...
  11. perplexabot

    A Derivative of log of normal distribution

    I have been trying to digest this notation that you have bestowed upon me. I can see its benefit and am willing to put some time to understand it better. I would like to know if you have some references for me that may help me better understand it? I am very thankful for your help : ) EDIT: By...
  12. perplexabot

    A Derivative of log of normal distribution

    Ok, since I am right in saying (along with your help in this older thread) that the PDF which describes the random variable, is itself (the pdf) not random but made up of "ordinary" variables, then after taking the derivative we will once again end up with a function that does NOT contain random...
  13. perplexabot

    A Derivative of log of normal distribution

    NOTE: If you don't want to read this whole post, just read "EDIT2," it contains the questions and remarks I have concluded. Everything else is just my train of thought. Hmmm, are those functions not the same, given that \phi_{k+1}=\phi_{k}+v_k with...
  14. perplexabot

    A Derivative of log of normal distribution

    Hey all, I've had this point of confusion for a bit and I have thought that with time I may be able to clear it out myself. Nope, hasn't happened. I think I need help. Let us say we have the following \phi_{k+1}=\phi_{k}+v_k where, v_k\overset{iid}{\sim}\mathcal{N}(0,\sigma^2) and...
  15. perplexabot

    Not sure how to solve matrix/equation system

    Nice! First, you may find it useful to know that the system of equations you have is a homogeneous system (Ax = b, where b = 0). Let me ask you a few questions. Bear with me. Do you know what a trivial solution is? Do you know what a non-trivial solution is? A homogeneous system always has at...
  16. perplexabot

    A Hessian of f(x)^T*Q*y

    Hmmm. I find your post interesting. I do not understand how you achieved your equations. Maybe my question was badly worded, or maybe I have truncated too much information from the question. Your final answer, f not necessarily being linear, is what I also think. Would it be wise to link or post...
  17. perplexabot

    Not sure how to solve matrix/equation system

    Your initial linear system is as follows: \ \ \ \ \ \ x+6y-18z=0\\ -4x+0y+\ \ 5z=0\\ -3x+6y-13z=0\\ -2x-2y+\ \ \ \ z=0 Your linear equation Ax=b would be: \begin{bmatrix} 1 & 6 & -18\\ -4 & 0 & 5\\ -3&6 &-13\\ -2&-2&1 \end{bmatrix} \begin{bmatrix} x\\ y\\ z \end{bmatrix} = \begin{bmatrix} 0\\...
  18. perplexabot

    Not sure how to solve matrix/equation system

    First try and formulate your problem as a linear equation (such as Ax=b). Next step, as you said, reduce it so that it is in row echelon form (not necessarily rref) and figure it out from there. I would also say try and do a little research first before you post : p
  19. perplexabot

    A Hessian of f(x)^T*Q*y

    Hey all. Let me just get right to it! Assume you have a function f:\mathbb{R}^n\rightarrow\mathbb{R}^m and we know nothing else except the following equation: \triangledown_x\triangledown_x^Tf(x)^TQy=0 where \triangledown_x is the gradient with respect to vector x (outer product of two gradient...
  20. perplexabot

    A What is the identity?

    I know this post is kind of old but I think it may be worth posting the answer (yes, I found it!) for future reference. So excuse the necromancy : p My logic was correct here, what was manipulated was indeed (J_n+D_n^{11})^{-1}. And as this thread's title suggests, it is an Identity that was...
  21. perplexabot

    A Conditional expectation and covariance of function of RVs

    Wow! Just WOW!!! I cannot explain how much both your last posts have helped me. You have cleared up some serious amount of confusion I have been carrying for a while. I am very thankful for your time. Tremendously valuable information! Thank you andrewkirk! Thank you Stephen Tashi!
  22. perplexabot

    A Conditional expectation and covariance of function of RVs

    I have one more question if I may. Let us use the following equation (the same one from above): x_{k+1}=x_k + v_{k+1}, where once again, v_{k+1}\sim\mathcal{N}(0,\sigma_v^2). It can be shown that E[x_{k+1}|x_k]=x_k and that cov(x_{k+1}|x_k)=\sigma_v^2. Now, substituting and setting up the normal...
  23. perplexabot

    A Conditional expectation and covariance of function of RVs

    Wow, that definitely expanded my general knowledge of derivatives. I have never even heard of these extensions you speak of. Very cool! Thank you : ) Once again thank you for directing me in the right direction. Your help is much appreciated. Thank you all.
  24. perplexabot

    A Conditional expectation and covariance of function of RVs

    First, thank you for all the help and clarification. ARMA, as you said, is where the current value of the process is a linear combination of past values plus an additive noise. BUT, if I am not mistaken, ARMA also depends on past shocks, or past noise values. This can be seen in wiki. I still...
  25. perplexabot

    A Conditional expectation and covariance of function of RVs

    Thank you! That makes more sense now. Does one ever differentiate with respect to the random variable (using the notation you provided, \frac{\partial}{\partial Y} rather than \frac{\partial}{\partial y})? I am thinking of cases such as the fisher information matrix. Hmmm, I see your point, so...
  26. perplexabot

    A Conditional expectation and covariance of function of RVs

    Thank you very much! I now realize why v_{k+1} and \epsilon_{k+1} must be independent and that I must include this in my assumptions. : ) That's great help! Now if I may ask my follow up question about differentiating with respect to a conditioned variable. Let f(x,y) be a function of random...
  27. perplexabot

    A Conditional expectation and covariance of function of RVs

    Hey all, I have been doing some math lately where I need to find the conditional expectation of a function of random variables. I also at some point need to find a derivative with respect to the variable that has been conditioned. I am not sure of my work and would appreciate it if you guys can...
  28. perplexabot

    I Gradient of ||f(x)||^2

    My work is wrong! Here is the correct method for the sake of completeness. \begin{equation*} \begin{split} \triangledown_x ||f(x)||^2_2 &=\triangledown_x (f(x)^Tf(x)) \\ &=(\triangledown_xf(x)^T)^Tf(x)+(\triangledown_xf(x))^Tf(x) \\ &=(\triangledown_xf(x))^Tf(x)+(\triangledown_xf(x))^Tf(x) \\...
  29. perplexabot

    I Gradient of ||f(x)||^2

    So I have made a couple of fixes, specifically making sure the matrix multiplaction agrees "dimensionally" \triangledown_x ||f(x)||^2_2=\frac{2f(x)^T}{||f(x)||_2}(\triangledown_xf(x)) I wonder if this is correct now. Anyone?
  30. perplexabot

    I Gradient of ||f(x)||^2

    So, I was washing the dishes when I realized that 2\triangledown_xf(x)^T \frac{f(x)^T}{||f(x)||_2} is not a scalar. This is because \triangledown_xf(x)^T is a matrix (this is actually the jacobian!). So now I have a feeling the above may be close, but still wrong. I would appreciate a...
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