Eigenspace vs. Eigenvector — What's the Difference?

(linear algebra) The linear subspace consisting of all eigenvectors associated with a particular eigenvalue, together with the zero vector.

A vector whose direction is unchanged by a given transformation and whose magnitude is changed by a factor corresponding to that vector's eigenvalue. In quantum mechanics, the transformations involved are operators corresponding to a physical system's observables. The eigenvectors correspond to possible states of the system, and the eigenvalues to possible observed values.

(linear algebra) given a linear transformation $A$, a vector $x$ such that $Ax=\backslash lambda\; x$ for some scalar $\backslash lambda$

(linear algebra) specifically, given a matrix A, the eigenvector of the transformation "left-side multiplication by A"