eigenspace Definition
a subspace of a vector space consisting of all eigenvectors corresponding to a particular eigenvalue.
Using eigenspace: Examples
Take a moment to familiarize yourself with how "eigenspace" can be used in various situations through the following examples!
Example
The eigenspace of the matrix A corresponding to the eigenvalue λ is the set of all solutions to the equation (A-λI)x=0.
Example
The eigenspace of the linear transformation T corresponding to the eigenvalue λ is the nullspace of the matrix (T-λI).
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Summary: eigenspace in Brief
An 'eigenspace' [ˈaɪɡən speɪs] is a subspace of a vector space that consists of all eigenvectors corresponding to a particular eigenvalue. It is used in linear algebra to solve equations involving matrices and linear transformations.
