A proof of Crouzeix's conjecture for a class of matrices

作者：Choi Daeshik^*

来源：Linear Algebra and Its Applications, 2013, 438(8): 3247-3257.

DOI：10.1016/j.laa.2012.12.045

• Crouzeix's conjecture
• Numerical range
• Field of values
• Jordan blocks

Crouzeix's conjecture is that for any square matrix A and any polynomial p we have
vertical bar vertical bar p(A)vertical bar vertical bar <= 2 max{vertical bar P(z)vertical bar : z epsilon W (4)} where W(A)],
is the field of values of A and vertical bar vertical bar . vertical bar vertical bar denotes the spec-tral norm. In this paper, we show that the conjecture holds for the matrices of the form
[GRAPHICS]
where lambda epsilon C and alpha = (alpha(1),, alpha(n)) epsilon C-n. Published by Elsevier Inc.

• 出版日期2013-4-15