Convert .mkv 1080p high definition film to play with a stand alone player HD

Hi,
            I have some .mkv files in high resolution 1080p, I want to play these files into my dvd/divx player that have a HDMI Output for high resolution 1080p too. The stand alone player doesn't have a blueray but dvd-dl and usb2.0. If I have to convert the .mkv into something else, what is the best way and tools to use (commercial and free) the permit a not loose of quality and a playback in the same high definition such 1080p in my tv?


Thanks a lot and sorry for my bad English (I'm Italian).

I have read a lot of documents around but no one is clear about high definition videos conversion.

Marco

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