All Questions
7 questions
24
votes
7
answers
16k
views
Expected determinant of a random NxN matrix
What is the expected value of the determinant over the uniform distribution of all possible 1-0 NxN matrices? What does this expected value tend to as the matrix size N approaches infinity?
- 251
13
votes
2
answers
879
views
The expected square of the determinant of a random row stochastic matrix
In this
question Anthony Quas asks about the expected absolute value of
the determinant of an $n\times n$ row stochastic matrix $A$, where
the rows are independently selected from the uniform ...
- 50.8k
6
votes
2
answers
738
views
Probability of a large random integer Matrix to have zero determinant
Suppose we have a matrix $A \in \{0,1\}^{n \times n}$ where
$$A_{ij} = \begin{cases} 1 & \text{with probability} \quad p\\ 0 &\text{with probability} \quad 1-p\end{cases}$$
I would like to ...
- 355
4
votes
1
answer
781
views
Determinant of a random row stochastic matrix
Does anyone know anything about the determinant of a random $n\times n$ row stochastic matrix? What I have in mind is that the rows are independently selected from the uniform distribution on the unit ...
- 23.2k
2
votes
0
answers
62
views
What is the distribution of determinant of multi multiplication of some Gaussian matrices?
I have a square matric $H = (ABC)(ABC)^H$ where $A$ and $C$ are complex Gaussian matrices with some correlation matrices and $B$ is a diagonal matrix with entries $e^{j \theta}$ on the diagonal such ...
1
vote
1
answer
1k
views
Expected size of determinant of $AA^T$ for non-square random $A$
If $A$ is chosen uniformly at random over all possible $m \times n$ (0,1)-matrices, what is the expected size of the absolute value of the determinant of $AA^T$. We can assume $m < n$ and all ...
- 3,377
1
vote
0
answers
90
views
How to prove that $\|A^tv\|_2 \leq \|Av\|_2^t$ for every $0<t<1$? [closed]
Consider a unit norm $\|V\|_2=1$ and a symmetric matrix $A$.
I wish to prove that $\|A^tv\|_2 \leq \|Av\|_2^t$ for every $0<t<1$.
My belief is that this is true is motivated by empirical ...
- 11