I have trouble understanding why the following theorem holds.


I am hoping someone can give me some idea, or logic behind why this holds.

I am not necessarily looking for a proof. What I am looking for is something which makes me grasp the idea so that I can see why this holds.

Obviously I can learn this by heart, but it would be pleasing to know what I am actually checking.

 Mar 25, 2014
I'm a bit out of my depth here (well, ok, a lot out of my depth!), but I think I might try to get an understanding by generating some specific examples using small matrices; e.g. choosing n = 3 and m = 1, say, so that A is a 3x3 matrix, B is a 1x3 vector, O is just the scalar 0, H is a 4x4 matrix and k would have just two values, 0 and 1. Fill A and B with some (randomly chosen?) test values to see if you can generate values that satisfy each of your three conditions in turn. I don't know if this is feasible, or even if it helps if it is, but it's the best I can come up with!
 Mar 25, 2014

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