Matrix/22/C/Orthonormal basis of eigenvectors/1/Exercise

Determine whether there exists, for the linear mapping ${}\mathbb {C} ^{2}\rightarrow \mathbb {C} ^{2}$ given by the matrix

${\begin{pmatrix}2-3{\mathrm {i} }&4+5{\mathrm {i} }\\11-3{\mathrm {i} }&6+9{\mathrm {i} }\end{pmatrix}},$

an orthonormal basis of ${}\mathbb {C} ^{2}$ consisting of eigenvectors.

Create a solution