Linear algebra matrix types complex matrices

mat = {{11., 3.}, {3., 5.}};
matG = CholeskyDecomposition[mat];
Transpose[matG].matG//MatrixForm

MatrixForm[{{11., 3.}, {3., 4.999999999999999}}]

mat = {{11., 3. + 2.I}, {3. - 2.I, 5.}};
matG = CholeskyDecomposition[mat];
Conjugate[Transpose[matG]].matG//MatrixForm

MatrixForm[{{11., 3. + 2.*I}, {3. - 2.*I, 1.1818181818181819 + 0.*I + Sqrt[3.8181818181818183 + 0.*I]*Conjugate[Sqrt[3.8181818181818183 + 0.*I]]}}]