Complex MatricesComplex matrices in Mathematica are defined in a way that is completely consistent with other types of matrices such as those that involve real numbers. All the functions that work for real matrices work for complex matrices. One special detail about complex matrices is that certain linear algebra computations that involve a transpose for real matrices involve a conjugate transpose for complex matrices. An example of this is the Cholesky decomposition. For a real symmetric positive definite matrix it is defined as shown below. In[1]:=  |
Out[3]//MatrixForm=
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For a complex hermitian positive definite matrix the definition is shown as follows. In[4]:=  |
Out[6]//MatrixForm=
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