eigensruimte
Eigensruimte, also known as the eigenspace, is a fundamental concept in linear algebra. For a given linear transformation, represented by a square matrix, an eigensruimte associated with a particular eigenvalue is the set of all eigenvectors corresponding to that eigenvalue, along with the zero vector. Formally, if A is a square matrix, lambda is an eigenvalue, and v is a corresponding eigenvector, then Av = lambda v. The eigensruimte for lambda, denoted E_lambda, is the set of all vectors x such that Ax = lambda x. This can be rewritten as Ax - lambda x = 0, or (A - lambda I)x = 0, where I is the identity matrix. This means the eigensruimte is precisely the null space (or kernel) of the matrix (A - lambda I).
An eigensruimte is always a subspace of the vector space on which the linear transformation is defined.