On the zero set of the Kobayashi–Royden pseudometric of the spectral unit ball
Volume 93 / 2008
Annales Polonici Mathematici 93 (2008), 53-68
MSC: Primary 32F45; Secondary 32A07.
DOI: 10.4064/ap93-1-4
Abstract
Given $A\in {\mit\Omega} _n,$ the $n^2$-dimensional spectral unit ball, we show that if $B$ is an $n\times n$ complex matrix, then $B$ is a “generalized” tangent vector at $A$ to an entire curve in ${\mit\Omega} _n$ if and only if $B$ is in the tangent cone $C_A$ to the isospectral variety at $A.$ In the case of ${\mit\Omega} _3,$ the zero set of the Kobayashi–Royden pseudometric is completely described.
