Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Crouzeix's conjecture holds for tridiagonal $3\times 3$ matrices with
  elliptic numerical range centered at an eigenvalue   M. Crouzeix formulated the following conjecture in (Integral Equations
Operator Theory 48, 2004, 461--477): For every square matrix $A$ and every
polynomial $p$, $$
  \|p(A)\| \le 2 \max_{z\in W(A)}|p(z)|, $$ where $W(A)$ is the numerical range
of $A$. We show that the conjecture holds in its strong, completely bounded
form, i.e., where $p$ above is allowed to be any matrix-valued polynomial, for
all tridiagonal $3\times 3$ matrices with constant main diagonal: $$
  \left[\begin{matrix}a&b_1&0\\c_1&a&b_2\\0&c_2&a\end{matrix}\right],\qquad
a,b_k,c_k\in\mathbb C, $$ or equivalently, for all complex $3\times 3$ matrices
with elliptic numerical range and one eigenvalue at the center of the ellipse.
We also extend the main result of D. Choi in (Linear Algebra Appl. 438,
3247--3257) slightly.

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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol