semiorthogonal

English

Etymology

From semi- +‎ orthogonal.

Adjective

semiorthogonal (not comparable)

1. (mathematics, category theory) Having the property that every subcategory is in the set of orthogonal subcategories of every higher order subcategory.
   • 2015, Asher Auel, Marcello Bernardara, “Semiorthogonal decompositions and birational geometry of del Pezzo surfaces over arbitrary fields”, in arXiv‎^[1]:

     For del Pezzo surfaces of degree at least 5, we construct explicit semiorthogonal decompositions by subcategories of modules over semisimple algebras arising as endomorphism algebras of vector bundles and we show how to retrieve information about the index of the surface from Brauer classes and Chern classes associated to these vector bundles..

2. (mathematics, matrix algebra) Either columnwise orthogonal (having the property that M'M is an identity matrix) or rowwise orthogonal (having the property that MM' is an identity matrix).
3. (physics) Orthogonal to the corresponding approximation space.