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A = [ 3.3+6.2i 7.1+9.1i 2.3+8.2i -3.2+6.6i;
-2.3+3.6i 0.3+9.7i 1.9+-4.9i 7.1+7.1i;
6.7+-0.1i 1.1+4.8i -9.7+3.7i -0.01+-0.2i;
8.4+7.7i 5.9+-1.8i 8.8+9.9i 0+0.1i;
]
B = [ 1.1+2.2i 3.3+4.4i 1.2+2.3i 3.4+4.5i;
8.8+7.7i 6.6+5.5i 3.5+7.2i -0.3+6.1i;
6.1+8.2i 9.7+3.6i -5.1+6.1i 2.3+8.1i;
6.3+2.9i 5.5+8.1i 8.5+6.7i 9+2.4i;
]
C = A * B
(-110.110,250.010) (-97.850,232.290) (-184.140,104.870) (-180.090,165.720)
(-6.590,137.580) (-57.190,123.300) (-46.850,179.640) ( 7.640,85.870)
(-108.683, 7.081) (-102.435,66.669) ( 5.715,-39.797) (-58.270,-36.804)
(30.290,189.720) (91.590,211.200) (-79.960,68.780) (-57.070,195.460)
C * B
(-6919.199,975.010) (-7883.329,1142.554) (-5063.800,-1300.820) (-6178.540,-503.102)
(-3722.331,2056.288) (-3437.379,3032.270) (-2779.525,-251.145) (-3076.656,877.121)
(-1449.081,-1030.123) (-1256.229,-1618.081) (-1020.338,-1211.081) (-877.937,-1626.178)
(-3182.440,3668.914) (-4212.248,3649.090) (-3406.522,2136.486) (-3790.311,2409.382)
D = A' * A
(242.330, 0.000) (156.670,-65.660) (121.210,56.450) (40.313,-0.771)
(156.670,65.660) (289.700, 0.000) (85.180,142.270) (107.189, 9.658)
(121.210,-56.450) (85.180,-142.270) (383.380, 0.000) (25.807,92.557)
(40.313, 0.771) (107.189,-9.658) (25.807,-92.557) (154.670, 0.000)
inverse(D)
( 0.008, 0.000) (-0.006, 0.001) (-0.001, 0.002) ( 0.003, 0.001)
(-0.006,-0.001) ( 0.018, 0.000) (-0.001,-0.010) (-0.017, 0.002)
(-0.001,-0.002) (-0.001, 0.010) ( 0.010, 0.000) ( 0.000,-0.012)
( 0.003,-0.001) (-0.017,-0.002) ( 0.000, 0.012) ( 0.024, 0.000)
[v,d] = eig(D);
diag(d)
21.695 114.964 297.042 636.378
v'
( 0.167, 0.000) (-0.581,-0.074) (-0.005, 0.394) ( 0.688, 0.029)
( 0.829, 0.000) (-0.302, 0.197) (-0.172,-0.198) (-0.327, 0.086)
( 0.236, 0.000) ( 0.420,-0.151) (-0.582,-0.143) ( 0.381,-0.491)
( 0.479, 0.000) ( 0.518,-0.241) ( 0.584, 0.275) ( 0.139, 0.083)
v * v'
( 1.000, 0.000) ( 0.000, 0.000) ( 0.000, 0.000) ( 0.000, 0.000)
( 0.000, 0.000) ( 1.000, 0.000) ( 0.000, 0.000) ( 0.000, 0.000)
( 0.000, 0.000) ( 0.000, 0.000) ( 1.000, 0.000) ( 0.000, 0.000)
( 0.000, 0.000) ( 0.000, 0.000) ( 0.000, 0.000) ( 1.000, 0.000)
sqrtm(D)
(14.249, 0.000) ( 4.839,-1.835) ( 3.176, 1.293) ( 0.852,-0.206)
( 4.839, 1.835) (14.680, 0.000) ( 2.138, 4.539) ( 4.715,-0.063)
( 3.176,-1.293) ( 2.138,-4.539) (18.171, 0.000) ( 0.469, 4.007)
( 0.852, 0.206) ( 4.715, 0.063) ( 0.469,-4.007) (10.742, 0.000)
sqrtm(D) * sqrtm(D)
(242.330, 0.000) (156.670,-65.660) (121.210,56.450) (40.313,-0.771)
(156.670,65.660) (289.700, 0.000) (85.180,142.270) (107.189, 9.658)
(121.210,-56.450) (85.180,-142.270) (383.380, 0.000) (25.807,92.557)
(40.313, 0.771) (107.189,-9.658) (25.807,-92.557) (154.670, 0.000)
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