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The magneto-optical properties of (Ga,Mn)As have been determined withindensity functional theory using the highly precise full-potential linearaugmented plane wave (FLAPW) method. A detailed investigation of the electronicand magnetic properties in connection to the magneto-optic effects is reported.The spectral features of the optical tensor in the 0-10 eV energy range areanalyzed in terms of the band structure and density of states and the essentialrole of the dipole matrix elements is highlighted by means of Brillouin zonedissection. Using an explicit representation of the Kerr angle in terms of realand imaginary parts of the tensor components, a careful analysis of the Kerrspectra is also presented. The results of our study can be summarized asfollows: i) different types of interband transitions do contribute in shapingthe conductivity tensor; ii) the dipole matrix elements are important inobtaining the correct optical spectra; iii) different regions in theirreducible Brillouin zone contribute to the conductivity very differently; iv)a minimum in the Re $\sigma_{xx}$ spectra can give rise to a large Kerrrotation angle in the same energy region; and v) materials engineering via themagneto-optical Kerr effect is possible provided that the electronic structureof the material can be tuned in such a way as to \emph{enhance} the depth ofthe minima of Re $\sigma_{xx}$.

Magneto-optical properties of (Ga,Mn)As: an ab--initio determination