August 25, 2014
>> A=[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1; 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0; 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1; 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1; 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1; 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0; 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0; 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0; 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1; 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0; 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1]; >> B = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1; 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0; 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1; 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0; 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0; 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0; 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1; 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1; 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1; 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0; 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1; 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0;] >> G = [Z A Z B;A' Z B' Z;Z B Z A;B' Z A' Z]; >> eig(G) ans = -12.0000 -3.4641 -3.4641 -3.4641 -3.4641 -3.4641 -3.4641 -3.4641 -3.4641 -3.4641 -3.4641 -3.4641 -3.4641 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 3.4641 3.4641 3.4641 3.4641 3.4641 3.4641 3.4641 3.4641 3.4641 3.4641 3.4641 3.4641 12.0000 >> % 3.4641^2 = 12
>> A = [1 1 1 1; 1 1 0 0;1 0 1 0; 1 0 0 1]; >> B = [0 0 0 0; 0 0 1 1;0 1 0 1; 0 1 1 0]; >> (A-B)*(A-B)' ans = 4 0 0 0 0 4 0 0 0 0 4 0 0 0 0 4 >> >> G = [Z A Z B;A' Z B' Z;Z B Z A;B' Z A' Z]; >> eig(G) ans = -4.0000 -2.0000 -2.0000 -2.0000 -2.0000 -0.0000 -0.0000 -0.0000 0.0000 0.0000 0.0000 2.0000 2.0000 2.0000 2.0000 4.0000
Comments Off on Spectrum of Hadamard Graphs
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