All Questions
7 questions with no upvoted or accepted answers
3
votes
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225
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Eigenvalues of Hadamard product of two Wishart-type matrices
Given two independent Gaussian matrices with i.i.d. entries: $A\in\mathbb{R}^{n\times p}$ and $B\in\mathbb{R}^{n\times q}$, where and $A_{i,j},B_{i,j}\sim\mathcal{N}(0,1)$. Assume that $\max(p,q)<n....
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2
votes
0
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100
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On a random matrix construction
Given a symmetric matrix $M\in\Bbb Z^{n\times n}$ or rank $r$ with absolute value of any entry bound by $2^{b^2-1}-1$ and maximum eigenvalue at most $\lambda$.
We consider the set $\mathcal T_b$ of $\...
- 13.9k
2
votes
2
answers
215
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How to analyze the value of convergence of functions of random matrices?
Consider a random i.i.d matrix $\mathbf{A}_{m\times n}$ with entries generated from a complex Gaussian distribution with zero mean and unit variance. I am interested in the large dimension analysis of ...
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1
vote
0
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40
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Asymptotic unitary invariance of rank-one spiked Gaussian matrix
I'm working on some Random Matrix Theory related stuff for my thesis, and i've come across the following problem:
Consider a (normalized) spiked Wigner matrix $\mathbf{A}$
$$ \mathbf{A} = \frac{\beta}{...
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1
vote
0
answers
46
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the 3th and 4th order statistics of Circularly Symmetric Complex Normal random vector?
Assume that ${\bf{z}} \in {\mathbb{C}}^{n \times 1}$ is a CSCG random vector denoted with $\mathcal{C} ~ (\bf{\mu} _0,\bf \Sigma _0)$ where $\mu _0$ and $\bf \Sigma _0$ are mean and contrivance matrix,...
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0
votes
0
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92
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Linear independence of Wishart matrices
Let $W\sim W_n(I,d)$ be a real Wishart matrix of an identity covariance matrix and $d$ degrees of freedom, i.e., $W=XX^T$ for $X$ being an $n\times d$ matrix whose entries are i.i.d sampled from a ...
- 123
0
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132
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Upper bound on the condition number of the product of a random sparse matrix and a semi-orthogonal matrix
Let $G \in \mathbb{R}^{n \times m}$ (m > n, m = O(n)) whose all entries are i.i.d. distributed as $\mathcal{N}(0, 1) * \text{Ber}(p)$. Let $V \in \mathbb{R}^{m \times n}$ be a fixed semi-orthogonal ...
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