Determinant of a Complex Matrix

[EngWiPy]

Hi,

Is det(A*)=(det(A))*, and why? Here ()* means complex conjugate only, and A is a complex matrix.

Thanks in advance

 

[Citan Uzuki]

Yes. The determinant is a polynomial with real coefficients of the entries in A, and for any polynomial p in n variables with real coefficients, p(x_1*, x_2*, ... , x_n*) = p(x_1, x_2, ... , x_n)*.

 

[EngWiPy]

Yes. The determinant is a polynomial with real coefficients of the entries in A, and for any polynomial p in n variables with real coefficients, p(x_1*, x_2*, ... , x_n*) = p(x_1, x_2, ... , x_n)*.

Ok I see. Thanks a lot

Regards