# Feng Liu

## Publications

##### 1 Several Spectrally Non-Arbitrary Ray Patterns of Order 4

**Authors:**
Ling Zhang,
Feng Liu

**Abstract:**

A matrix is called a ray pattern matrix if its entries are either 0 or a ray in complex plane which originates from 0. A ray pattern *A *of order *n *is called spectrally arbitrary if the complex matrices in the ray pattern class of *A* give rise to all possible *n*th degree complex polynomial. Otherwise, it is said to be spectrally non-arbitrary ray pattern*.* We call that a spectrally arbitrary ray pattern *A *of order *n *is minimally spectrally arbitrary if any nonzero entry of *A* is replaced, then *A *is not spectrally arbitrary. In this paper, we find that is not spectrally arbitrary when n equals to 4 for any θ which is greater than or equal to 0 and less than or equal to n. In this article, we give several ray patterns A(θ) of order n that are not spectrally arbitrary for some θ which is greater than or equal to 0 and less than or equal to n. by using the nilpotent-Jacobi method. One example is given in our paper.

**Keywords:**
spectrally arbitrary,
nilpotent matrix,
ray patterns,
sign patterns

## Abstracts

##### 1 Several Spectrally Non-Arbitrary Ray Patterns of Order 4

**Authors:**
Ling Zhang,
Feng Liu

**Abstract:**

*A*of order

*n*is called spectrally arbitrary if the complex matrices in the ray pattern class of

*A*give rise to all possible

*n*th degree complex polynomial. Otherwise, it is said to be spectrally non-arbitrary ray pattern

*.*We call that a spectrally arbitrary ray pattern

*A*of order

*n*is minimally spectrally arbitrary if any nonzero entry of

*A*is replaced, then

*A*is not spectrally arbitrary. In this paper, we find that is not spectrally arbitrary when n equals to 4 for any θ which is greater than or equal to 0 and less than or equal to n. In this article, we give several ray patterns A(θ) of order n that are not spectrally arbitrary for some θ which is greater than or equal to 0 and less than or equal to n. by using the nilpotent-Jacobi method. One example is given in our paper.

**Keywords:**
spectrally arbitrary,
nilpotent matrix,
ray patterns,
sign patterns