Are Eigenspaces and Eigenvectors the Same Thing?

is that eigenspace is (linear algebra) a set of the eigenvectors associated with a particular eigenvalue, together with the zero vector while eigenvector is (linear algebra) a vector that is not rotated under a given linear transformation; a left or right eigenvector depending on context.

Does an eigenspace consist of only eigenvectors?

The eigenspace Eλ consists of all eigenvectors corresponding to λ and the zero vector. A is singular if and only if 0 is an eigenvalue of A. The nullity of A is the geometric multiplicity of λ=0 if λ=0 is an eigenvalue.

What are the Eigenspaces?

Vibration analysis – Eigenspace describes the shapes of the vibration modes of an object for each eigenvalue or natural frequency, referred to in this context as an eigenfrequency.