Recent content by hadron23

Hello, This is probably an extremely simple question and my lack of sleep is preventing me from understanding it completely, but I figured I would ask. Suppose you have one fair die. You roll it 3 times. What is the probability that the first and second roll are the same number? My guess is...

Hi, I proved the following statement by induction. Does anyone see any oversights or glaring errors? It is for a class where the homework is assigned but not collected, and I just want to know if I did it right. ThanksQUESTION: Consider the stochastic process \{X_t,\,t=0,1,2,\ldots\} described...

I suppose all hyperbolas have asymptotes of equal slope magnitude but opposite sign, since they can just be thought of as a vertical conic cross section. The function I am after essentially has to look like exp(x) for negative x and be linear for positive x. Think of an exponential function...

Hello, I wish to find a function similar to, y^2-x^2=1 but instead of the slope of the asymptotes being +/- 1, I need one of the asymptotes to be of slope 0. That is, I wish to find a hyperbolic function with one horizontal asymptote and the other of slope 1. Is this possible?

In hindsight, this is stupidly simple. Thanks!

Hello, I have a row vector defined as, X=\{x_1,x_2,\ldots,x_L\} I wish to "stack" this vector vertically, a total of N times, such that the result is a matrix of the form, \begin{align}Y = \left[ \begin{array}{cccc} x_1 & x_2 & \ldots & x_L \\ x_1 & x_2 & \ldots & x_L \\ . & . & . & .\\ . & ...

Hello, I have an observation model that generates a vector of state estimates (of the true underlying states) and a corresponding error covariance matrix. I have a function called f(), which operates on the state estimate to return a scalar value. Note that I do not know the true state, only...

Did you ever get bored in your off time? I know there is no shortage of things to do in Montreal, but I'm not sure if I can say the same about Ann Arbor...

Thanks for the quick reply. I did leave out some details. I have been offered a fellowship at UMich (tuition waiver and stipend), which includes health care coverage. I am still waiting on if I will be offered any funding beyond tuition and living expenses (bare minimum) at McGill.

Hello, I am a master's student in electrical engineering at one of the top 3 schools in Canada (prefer not to disclose just for privacy). I have applied to a few places for a PhD and have heard back from a couple. I am trying to choose between two schools, McGill or the University of...

Hi, I have just started using Mathematica mainly for its symbolic math abilities; however, I have run into a small problem that I don't know how to fix. I have generated a matrix of dimensions: Dimensions[A] = {4,4,1} And I need to convert this to a matrix of dimensions...

Hello, I am trying to come up with an expression for a bound on the sum of higher order terms, above second order. Consider the following Taylor expansion of a function f(x) around a point a, f(x) = f(a) + \frac{f^{(1)}(a)}{1!}(x-a) + \frac{f^{(2)}(a)}{2!}(x-a)^2+...

Hello All, I am currently a Master's student studying electrical engineering, specifically statistical signal processing and stochastic control. My work during my degree so far has primarily been applied to radar systems and the defence industry in general. I will be graduating next spring and...

I guess the a sufficient condition for this is if A>B then do all the eigenvalues of A dominate all of the eigenvalues of B?

Hi, Given two real-valued positive-definite matrices A and B, assume one is greater than the other with respect to positive definite ordering. That is, A>B. Does the following implication hold? A>B \Rightarrow \text{det}(A)>\text{det}(B) Thanks.