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Definition of eigenspace of a matrix
An eigenspace of a matrix is a nontrivial subspace.
An eigenspace of a matrix is the null space of a related matrix.

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An eigenspace of a matrix is a nontrivial subspace.

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The eigenspace of a linear transformation is a nontrivial subspace.Close match
Definition of eigenspace of a matrixClose match
Definition of eigenspace of a linear transformationClose match
EigenspacesClose match
An eigenspace of a matrix is the null space of a related matrix.Close match
The dimension of a eigenspace is less than or equal to the (algebraic) multiplicity of the eigenvalue.Close match
The eigenvalues of a matrix are the roots/solutions of its characteristic polynomial/equation.Close match
Definition of eigenvalue of a matrixClose match
Definition of eigenvector of a matrixClose match
Eigenvalues and operations on matricesClose match
The eigenvalues of a scalar multiple of a matrix are the scalar multiples of the eigenvalues.Close match
MultiplicityClose match
Definition of geometric multiplicity of an eigenvalueClose match
The left null space of a matrix is a subspace of R^m (or C^m).Close match
The eigenvalues of a power of a matrix are the power the eigenvalues.Close match
Definition of kernel of linear transformationClose match
Every nonzero finite-dimensional complex operator has an eigenvalueClose match
Subspaces associated to a linear transformationClose match
The eigenvalues of a polynomial of a matrix are the polynomial of the eigenvalues.Close match
Subspaces associated to a matrixClose match

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