Tagged Questions
1
vote
1answer
52 views
Expected value of a multivariate distribution
Given this random vector:
$$
\mathbf{x} = \begin{bmatrix} x_1 \\ x_2
\end{bmatrix}
$$
And this probability distribution function that takes it as argument:
$$
f_\mathbf{X}(\mathbf{x}) = ...
1
vote
1answer
40 views
Is Wishart Matrix?
Analyzing a system, I have faced a problem which is related to Random Matrices and in particular Wishart matrix. The problem is as follows:
Lets assume $\boldsymbol{H}$ is an $m\times n$ random ...
1
vote
0answers
31 views
How to determine the degrees of freedom of an inner-product matrix of two random matrices?
I have two random matrices A and B, with N columns each. The columns of A and B are independent but not necessarily identically distributed. A and B may be considered as two instances of an underlying ...
3
votes
0answers
54 views
Suboptimal confidence for bounds on the extreme eigenvalues of random matrices: can they be improved?
Typical results from the literature of Random Matrix Theory (RMT) (e.g., Tropp'11, Vershynin'12) provide probabilistic guarantees for large deviation of the extreme eigenvalues of random matrices like ...
2
votes
0answers
130 views
Slutsky's theorem for random matrices
This image is from Applied Multivariate Analysis. In this image plim means convergence in probability. I could not find the reference about the statement for ...
10
votes
1answer
243 views
spectral norm of random matrix
Suppose $A$ is a $n \times n$ random matrix with centered Gaussian (real) i.i.d entries with variance $\sigma^2/n$.
What to we know about the spectral norm $s(A)$ of $A$, that is $\sqrt{\rho(A^t A)}$ ...
1
vote
0answers
60 views
Studying the maxima of columns of a random matrix as a point process
Consider a matrix, $S$, of i.i.d. real RVs : $X_{ij}$ for $1 \leq i \leq s$, $1 \leq j \leq n$. Let $F$ denote the distribution of $X_{ij}$. For $1 \leq j \leq n$, consider $Y_{j}^{(1)} = \max_{i} ...
5
votes
1answer
124 views
Is there a simple argument for why a random symmetric matrix has distinct eigenvalues?
Lets generate a random symmetric matrix $A$ by generating the entries of a random matrix $Z$ iid from some continuous distribution, and setting $A=(1/2)(Z+Z^T)$. I think its true that $A$ should have ...
