There the following options in front of you as such:
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Utilize a PS 2 keyboard and use PS 2 protocol in your Arduino programme to handle inputs coming from keyboard strokes and as per the inputs you can code to light up the LED;s in matrix the way you want.(you can implement this feature without a computer dependency)
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You can write a processing programme or any other language programme which can intake the letter pressed on the keyboard and send to the serial port to which the arduino is connected.(computer dependency)
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Easiest way is to use a USB host shield with a USB keyboard that provides you a standalone keyboard without a computer and a bit easy to code as well.(w/o computer dependency).
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Nishant