Konvexního

Konvexního is the genitive singular form of the Czech adjective konvexní, meaning convex. The adjective konvexní describes geometric or analytical properties in mathematics, where an object is convex if the line segment between any two points in the object lies entirely within the object. This property is fundamental in geometry, analysis, and optimization.

The form konvexního is used to modify masculine inanimate nouns in the genitive case, for example in phrases like vlastnost konvexního tělesa, which translates to the property of a convex body. In Czech, other noun phrases describing convexity may use different adjective endings depending on gender and case, but konvexního is the standard genitive singular form for suitable masculine inanimate nouns.

In mathematical usage, konvexní appears in several key terms, including konvexní množina (convex set), konvexní obal (convex hull), konvexní funkce (convex function), and konvexní kombinace (convex combination). These concepts underpin convex geometry and convex optimization, where convexity ensures certain desirable properties such as the existence of global optima and tractable algorithms.

Etymology traces konvexní to Latin convexus, via French convex, with Czech morphological suffixing to form adjectives and nouns like konvexnost (convexity). The negation form nekonvexní is used for non-convex objects. Konvexnost remains a central notion across geometry, analysis, and optimization.