Definition for "Geometric Multiplicity" in the Quantum Dictionary

- Natural & Formal Sciences -

Mathematics & Logic Dictionary

The geometric multiplicity of an eigenvalue is the dimension of its eigenspace: the subspace of vectors v such that (A − λI)v = 0. It counts the maximum number of linearly independent eigenvectors associated with that eigenvalue.

- Pure Mathematics -

Algebra Dictionary

The dimension of the eigenspace associated to a given eigenvalue; equivalently, the number of linearly independent eigenvectors for that eigenvalue.