# Tagged Questions

260 views

### numerical range of a column-zero-sum matrix

I am trying to produce an example of a (necessarily non-normal) matrix that has only eigenvalues with positive real part, but whose numerical range contains elements with strictly negative real part. ...
255 views

### Eigenvalues of Sum of non-singular matrix and diagonal matrix

Suppose $D={\rm diag}(d_i)$ is a diagonal matrix with all diagonal entries $d_i=\pm 1$. This implies $D^2=I$. Suppose $A$ is a non-singular Hermitian matrix. If we know that $A+A^{-1}+D$ has rational ...
47 views

2k views

### Perron-Frobenius “inverse eigenvalue problem”

The Perron-Frobenius theorem says that the largest eigenvalue of a positive real matrix (all entries positive) is real. Moreover, that eigenvalue has a positive eigenvector, and it is the only ...
1k views

### Infinite hermitian matrix

Suppose we have a finite square n x n matrix of complex numbers H that is Hermitian and skew-symmetric: $H^\dagger = H$ and $H^T = -H$. (T denotes transpose, $\dagger$ denote conjugate transpose. I ...
I am interested in trying to design a Hermitian Jacobi (tridiagonal) matrix $H$ that has specific properties. The basic property, which is simple enough to construct, is that for an $N\times N$ matrix ...