# Tagged Questions

**3**

votes

**1**answer

176 views

### When is this matrix singular?

Consider matrix $A$ with $(j,k)$′th entry $A_{j,k}=\sin(\omega_j t_k+\phi_j),\,\forall j,k\in\{1,2,...,n\}$, where $\omega_j,t_k,\phi_j\in \mathbf R$.
1) For $t_k=k$, what is the condition on ...

**4**

votes

**1**answer

117 views

### Epidemic threshold

Need some help / ideas to proceed. Stuck for a while on this.
In the literature of epidemic theory, it is found that the epidemic threshold is $1/\lambda_{max}(A)$ where $\lambda_{max}(A)$ is the ...

**2**

votes

**1**answer

81 views

### Dimension independent computational complexity of singular value decomposition

Suppose $X$ is a $m \times n$ real matrix, which has only $k$ number of nonzero elements ($k \ll mn$).
Given a vector $y$, the sparsity of $X$ allows $X y$ to be computed in $O(k)$ time
which is ...

**0**

votes

**2**answers

204 views

### Eigenvalues of an amplification matrix

Let $A$ and $B$ square real matrices.
I know that the matrix $A+B$ has 1 as eigenvalue of multiplicity 1 and the others eigenvalues have their modulus <1.
Can we say something about the eigenvalues ...

**1**

vote

**0**answers

58 views

### Which matrix/operator in a cone has the largest negative spectral part?

Background:
Let $\mathcal{K}$ be set (convex cone, if you like) of symmetric matrices of order $n$. Each matrix $A \in \mathcal{K}$ can be decomposed in a unique way as $A=A_{+}-A_{-}$, where ...

**1**

vote

**2**answers

435 views

### can eigenvector be found without computing the eigenvalue [closed]

Is there any ways to compute the eigen vector without computing explicitly the associated eigenvalue?
Actually, I'd like to compute the largest eigenvalue of a positive matrix from its eigen vector, ...