Recent content by azay

Ok, I know the Fourier effect of a time shift is a multiplication with an exponential: x(t-t0) → exp(-j2∏f*t0)X(f) Now say Y(f) is the Fourier transform of y(t). What I am wondering what is the difference in the Fourier space when convolving Y(f) with either X(f) or exp(-j2∏f*t0)X(f)...

Given a homogeneous linear least squares problem: A^{T}y=0 What is the difference between minimizing y^{T}AA^{T}y (the least square error) and: y^{T}AA^{+}y=y^{T}A(A^{T}A)^{-1}A^{T}y ? Thanks.

Okay. Thanks for helping me out!

It was just a theoretical example. Why is it not possible to have probability 1 for all transitions except A->B and A->E? (the sum of the probabilities of A->B and A->E is obviously 1, with both being not equal to 0). There are no other transitions except the ones I listed. It is a valid Markov...

There are no other possible transitions. Only A->B and A->E are possible. The gcd is 2...

Yes, I had seen this pattern. I just found kind of quirky because in many places where they give intuition about this definition they say as if you can visit for every multiple of 2. But thanks for confirming :).

It's not possible to go from A to B to A in my example. Say: A->B->C->D->A (4 steps) is possible and A->E->F->...->A (18 steps) is possible. I don't see how it is possible to get back in 2 steps... What am I missing?

But in my example it is not possible to get back to state i in 2 steps, while 2 is the gcd. How does this make '2' the minimum? The minimum is '4'.

Hello, I am trying to understand the intuition of the definition of the period of a state in a Markov chain. Say for example we can go from state i to state i in either 4 steps or either 18 steps. gcd(4,18)=2, with gcd=greatest common divisor. So the period of state i is equal to 2. I...

From the central limit theorem the binomial distribution can be approximated by a normal distribution N(0,1). But the binomial distribution can also be approximated by a poisson distribition. Does this mean there is a relationship between the normal distribution and the poisson distribution...

Given the fact that the following inequality must hold; x > y-1 For all y \in ]0,1[ (an open interval) and given the fact that one can choose y After one chooses x, can one then state that x > 0 holds? My idea was to say that at least x >= 0 holds because: 1) Someone picks a negative x...

Thanks

It states in course notes: ------------------------------------------- If y = f(x) defines a surface in (n+1) dimensional space then the normal is defined as the (n+1)-dimensional vector: (\frac{\partial f(x)}{\partial x1},(\frac{\partial f(x)}{\partial x2},...,(\frac{\partial f(x)}{\partial...

In polynomial interpolation: I see some connection between: The Vandermonde matrix, the monomial basis and the fact that 'the monomial basis is not a good basis because it's components are not very orthogonal'. Now, I still don't really grasp sufficiently the reason why exactly a Vandermonde...

When approximating a function with a Taylor series, I understand a series is centered around a given point a, and converges within a certain radius R. Say for a series with center a the interval of convergence is [a-R, a+R]. Does this imply that: 1. There also exists a Taylor series expansion...