Let \(\Mtrx{A}\) be an \((n,n)\)-matrix with eigenvalue \(\EigenVal{\lambda}\). The eigenspace of \(\Mtrx{A}\) corresponding to \(\lambda\) is

\[\EigenSpc{\lambda} \DefEq \NullSpc{\Mtrx{A}- \EigenVal{\lambda} \cdot \IdMtrx{n} }\]

The geometric multiplicity of \(\EigenVal{\lambda}\) is \(\GmtrcMltplcty{\EigenVal{\lambda}} \DefEq \Dim{ \NullSpc{\Mtrx{A}-\EigenVal{\lambda}\cdot\IdMtrx{n}} }\).