The geometric multiplicity of an eigenvalue is defined as the dimension of the eigenspace associated with that eigenvalue. For a linear transformation T: V → V, if λ is an eigenvalue, the eigenspace E_λ is the set of all eigenvectors corresponding to λ, including the zero vector. The geometric multiplicity is crucial in understanding the behavior of linear transformations and is always less than or equal to the algebraic multiplicity of the eigenvalue.
PREREQUISITESStudents and professionals in mathematics, particularly those studying linear algebra, as well as engineers and data scientists working with systems that involve eigenvalue problems.