English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We define a leaf which is a domain in the closure$\overline{\mathfrak{H}}=\mathfrak{H}\cup\mathbb{R}\cup\{\infty\}$ of thecomplex upper half plane $\mathfrak{H} = \{z\in\mathbb{C}\mid{\mathrm{Im}\,}z>0\}$ for any linear transformation of an inner product space over the realnumber field $\mathbb{R}$. If the dimension of the inner product space is atleast 3, the leaf is convex on the Poincar\'e metric, and then simplyconnected, and contains all eigenvalues with nonnegative imaginary part.Moreover, if the linear transformation is normal, the leaf is the eigenvaluegeodesic polygon, which is the minimum convex domain in$\overline{\mathfrak{H}}$ containing all eigenvalues with nonnegative imaginarypart. We discuss the application of the geometric properties of a leaf to theoperator norm.

A leaf as a convex domain containing eigenvalues of a linear transformation on a real inner product space