Recent content by Jyupiter

I'm sorry for being unclear in my previous reply. What I meant by "self-swapping" is replacing a row in a matrix by itself, e.g. Row 2 swaps with Row 2. I have no idea what determinants are yet, but perhaps its because of this that "self-swapping" is not allowed? As you could always arbitrarily...

Thanks for the quick reply! What you said made sense. About the self-swapping row operation though, Hefferon's text stated that it's not allowed (said it has something to do with determinants later; I'm not that far into LA yet!). Is that restriction not the convention?

I'm just wondering, is an identity matrix, say I3 considered as an elementary matrix? It's obviously possible, since we can multiply any row of I with a constant 1. I'm just curious if there is a restriction for rescaling with a constant 1.

Lecturer revealed the solution: \hat{\beta}_k=arg\ max_\beta\ \prod_{i=1}^{N}\ \frac{1}{k^{2}+(x_{i}-\beta)^{2}} \Rightarrow \hat{\beta}_k=arg\ min_\beta\ \prod_{i=1}^{N}\ k^{2}+(x_{i}-\beta)^{2} \Rightarrow \hat{\beta}_k=arg\ min_\beta\ \sum_{i=1}^{N}\ ln\ (k^{2}+(x_{i}-\beta)^{2}) let...

Sure, why not? Do you think n!>1000^{n} for some large n to be true? If so, could you manipulate the rational function using this knowledge?

Correct me if I'm wrong, but the figure attached seems to hint at K=max\ \{ (\frac{k}{\pi})^{N}\ \prod_{i=1}^{N}\ \frac{1}{k^2+(x_{i}-\beta)^2}\}. Then x_{i}\rightarrow\beta\ \Rightarrow K=(\frac{1}{k\pi})^{N}\ \Rightarrow k^{N}\propto \frac{1}{K} and k\not = 0. (I'm sure this is flawed; surely...

Major Update! So I've spotted an error in the question, namely (2), which states k as a constant and a variable at the same time. I've reconciled this with my lecturer and it's confirmed that there's a misprint in the equation. (2) should actually look like this: \hat{\beta}_{k}=arg\...

The complete question reads like this: "Describe the effect of k on (2) corresponding to (1). The function in (2) can be read as the values of β that would maximize the function in (1) or argument that would maximize (1)." There's an accompanying image...

So I've apparently been given an assignment on Cauchy functions (it says here on the title), but I have no idea what that means. Nevertheless, here's my attempt to solve this problem: Given (1): f(x)=\frac{k}{\pi}\times\frac{1}{k^{2}+(x-\beta)^{2}} and (2): \hat{\beta}_{k}=arg\ max_{\beta}...