symmetric representation of ternary forms associated to some toeplitz matrices †
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ID: 246172
2018
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Abstract
Let A be an
n
×
n
complex matrix. Assume the determinantal curve
V
A
=
{
[
(
x
,
y
,
z
)
]
∈
CP
2
:
F
A
(
x
,
y
,
z
)
=
det
(
x
ℜ
(
A
)
+
y
ℑ
(
A
)
+
z
I
n
)
=
0
}
is a rational curve. The Fiedler formula provides a complex symmetric matrix S satisfying
F
S
(
x
,
y
,
z
)
=
F
A
(
x
,
y
,
z
)
. It is also known that every Toeplitz matrix is unitarily similar to a symmetric matrix. In this paper, we investigate the unitary similarity of the symmetric matrix S and the matrix A in the Fiedler theorem for a specific parametrized family of
4
×
4
nilpotent Toeplitz matrices A. We show that there are either one or at least three unitarily inequivalent symmetric matrices which admit the determinantal representation of the ternary from
F
A
(
x
,
y
,
z
)
associated to the specific
4
×
4
nilpotent Toeplitz matrices.
| Reference Key |
chien2018symmetrysymmetric
Use this key to autocite in the manuscript while using
SciMatic Manuscript Manager or Thesis Manager
|
|---|---|
| Authors | ;Mao-Ting Chien;Hiroshi Nakazato |
| Journal | journal of hospitality and tourism management |
| Year | 2018 |
| DOI |
10.3390/sym10030055
|
| URL | |
| Keywords | Keywords not found |
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