likeverdiprojeksjoner
Likeverdiprojeksjoner is a term used in Norwegian-language mathematical and data-science contexts to describe a class of projection operators that aim to preserve a specified value when projecting from a larger space to a smaller one. In practice, a projection P from a vector space V to a subspace W is called a likeverdiprojeksjon with respect to a valuation φ if and only if φ(Px) = φ(x) for every x in V. This makes the projection “value-preserving” with respect to the chosen valuation.
Formal considerations depend on the nature of φ. If φ is linear, the condition imposes concrete constraints on
Examples and variants: Orthogonal projections in Euclidean spaces preserve the inner product and, consequently, the norm,
Applications and scope: Likeverdiprojeksjoner are relevant to dimensionality reduction, model reduction in control theory, data compression,