Hwa-Long Gau

activity

20092026

most citedWeighted Shift Matrices: Unitary Equivalence, Reducibility and Numerical Ranges

23 citations · 64 across the 9 of their papers we have counts for

collaborators

10 papers

math.FA2026

Numerical radius of certain two-by-two block matrices

Hwa-Long Gau, Jia-Huo Hong, Chi-Kwong Li +1

We investigate the numerical range $W (T)$ and numerical radius $w (T)$ of operators of the form $T = (A 0 B 0)$ . We show that $W (T)$ is the union…

math.FA2014★ 1 cited

Upper and Lower Bounds for Numerical Radii of Block Shifts

Hwa-Long Gau, Pei Yuan Wu

For any $n$ -by- $n$ matrix $A$ of the form \[[\begin{array}{cccc} 0 & A_1 & & \\ & 0 & \ddots & \\ & & \ddots & A_{k-1} \\ & & & 0\end{array}],\] we consider two $k$ -by- $k$ matrices…

math.FA2013

Power Partial Isometry Index and Ascent of a Finite Matrix

Hwa-Long Gau, Pei Yuan Wu

We give a complete characterization of nonnegative integers $j$ and $k$ and a positive integer $n$ for which there is an $n$ -by- $n$ matrix with its power partial isometry index equ…

math.FA2013

Structures and Numerical Ranges of Power Partial Isometries

Hwa-Long Gau, Pei Yuan Wu

We derive a matrix model, under unitary similarity, of an $n$ -by- $n$ matrix $A$ such that $A, A^{2}, \dots, A^{k}$ ( $k \geq 1$ ) are all partial isometries, which generalizes the known f…

math.FA2013★ 9 cited

Numerical Radii for Tensor Products of Matrices

Hwa-Long Gau, Kuo-Zhong Wang, Pei Yuan Wu

For $n$ -by- $n$ and $m$ -by- $m$ complex matrices $A$ and $B$ , it is known that the inequality $w (A \otimes B) \leq ∥ A ∥ w (B)$ holds, where $w (\cdot)$ and $∥ \cdot ∥$ denote, respectively…

math.FA2013

Zero-dilation Index of a Finite Matrix

Hwa-Long Gau, Kuo-Zhong Wang, Pei Yuan Wu

For an $n$ -by- $n$ complex matrix $A$ , we define its zero-dilation index $d (A)$ as the largest size of a zero matrix which can be dilated to $A$ . This is the same as the maximum $k$ …

math.FA2013

Numerical Ranges of KMS Matrices

Hwa-Long Gau, Pei Yuan Wu

A KMS matrix is one of the form $$J_n(a)=[{array}{ccccc} 0 & a & a^2 &... & a^{n-1} & 0 & a & \ddots & \vdots & & \ddots & \ddots & a^2 & & & \ddots & a 0 & & & & 0{array}]$$ for $…

math.FA2012★ 15 cited

Higher-rank Numerical Ranges and Kippenhahn Polynomials

Hwa-Long Gau, Pei Yuan Wu

We prove that two n-by-n matrices A and B have their rank-k numerical ranges $Λ_{k} (A)$ and $Λ_{k} (B)$ equal to each other for all k, $1 \leq k \leq ⌊ n /2 ⌋ + 1$ , if and only if t…

math.FA2012★ 23 cited

Weighted Shift Matrices: Unitary Equivalence, Reducibility and Numerical Ranges

Hwa-Long Gau, Ming-Cheng Tsai, Han-Chun Wang

An $n$ -by- $n$ ( $n \geq 3$ ) weighted shift matrix $A$ is one of the form $$[{array}{cccc}0 & a_1 & & & 0 & \ddots & & & \ddots & a_{n-1} a_n & & & 0{array}],$$ where the $a_{j}$ 's, call…

math.FA2009★ 16 cited

Higher rank numerical ranges of normal matrices

Hwa-Long Gau, Chi-Kwong Li, Yiu-Tung Poon +1

The higher rank numerical range is closely connected to the construction of quantum error correction code for a noisy quantum channel. It is known that if a normal matrix $A \in M_…