Question

i have some eigenvalues, can somebody help me with eigenvectors

Answer 1

\[\mathbf T =\bigg(\array{1 & 1-i\\1+i & 0}\bigg)\]

Answer 2

Matrix T is hermitian \[\mathbf T ^\dagger = \mathbf { \tilde T^*} =\bigg( { {\tilde { \array{1 & 1-i\\1+i & 0}} \bigg)^* } }= \bigg( \array{1 & 1-i\\1+i & 0}\bigg) \]