Definition & Betydelse | Engelska ordet EIGENSPACE

Definition av EIGENSPACE

1. (matematik) egenrum

Exempel på hur man kan använda EIGENSPACE i en mening

• Indeed, if G acts on a vector space V over F, each simultaneous eigenspace for every element of G, if such exists, determines a multiplicative character on G: the eigenvalue on this common eigenspace of each element of the group.
• The dimension of the eigenspace corresponding to the eigenvalue 4 is 1 (and not 2), so A is not diagonalizable.
• There is also a collection of distinguished operators called Hecke operators on smooth functions on congruence covers, which commute with each other and with the Laplace–Beltrami operator and are diagonalisable in each eigenspace of the latter.
• A vector that is the sum of two or more non-zero vectors belonging to different eigenspaces will be tilted towards the eigenspace with largest eigenvalue.
• A central collineation is a homography defined by a (n+1) × (n+1) matrix that has an eigenspace of dimension n.
• Socle (mathematics), an algebraic object generated by minimal subobjects or by an eigenspace of an automorphism.
• Going beyond the linearization, when we account for perturbations by nonlinearity or forcing in the dynamical system, the center eigenspace deforms to the nearby center manifold.

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