POV-Ray : Newsgroups : povray.text.scene-files : [Minimum Volume] Bounding Ellipsoid via SVD : Re: [Minimum Volume] Bounding Ellipsoid via SVD Server Time
26 Sep 2021 06:56:52 EDT (-0400)
  Re: [Minimum Volume] Bounding Ellipsoid via SVD  
From: Bald Eagle
Date: 5 Nov 2019 21:40:00
Message: <web.5dc23255f7b9a3af4eec112d0@news.povray.org>
Looks like the nan values were because the matrix.resize operations didn't fill
in the new positions with 0.

Fixed it one way, until I needed to fix it another ;)

But now it runs without errors or nan entries.

So, now to see if any of this makes any sense in terms of processing a long list
of 3D vectors, and then plug it into the bounding ellipsoid code.

If this only processes square matrices, we'll probably need to use the gsl-bin
svd library to process the vectors.

But here we go  :)


Singular Value Decomposition (SVD):

Enter size of matrix N = (50x50 max): 10

A =
8.0 4.0 2.0 4.0 3.0 9.0 0.0 8.0 4.0 9.0
8.0 4.0 2.0 0.0 8.0 9.0 5.0 2.0 4.0 4.0
4.0 3.0 5.0 5.0 9.0 0.0 3.0 5.0 0.0 9.0
9.0 0.0 3.0 1.0 6.0 9.0 2.0 9.0 9.0 7.0
8.0 9.0 3.0 2.0 9.0 1.0 3.0 6.0 4.0 8.0
0.0 8.0 1.0 8.0 5.0 0.0 8.0 8.0 7.0 0.0
7.0 6.0 3.0 3.0 0.0 1.0 2.0 2.0 0.0 3.0
1.0 0.0 2.0 4.0 4.0 2.0 6.0 8.0 8.0 2.0
8.0 1.0 2.0 9.0 9.0 8.0 2.0 9.0 6.0 9.0
2.0 4.0 8.0 5.0 9.0 8.0 6.0 3.0 2.0 9.0


[matrix]transposed =
8.0 8.0 4.0 9.0 8.0 0.0 7.0 1.0 8.0 2.0
4.0 4.0 3.0 0.0 9.0 8.0 6.0 0.0 1.0 4.0
2.0 2.0 5.0 3.0 3.0 1.0 3.0 2.0 2.0 8.0
4.0 0.0 5.0 1.0 2.0 8.0 3.0 4.0 9.0 5.0
3.0 8.0 9.0 6.0 9.0 5.0 0.0 4.0 9.0 9.0
9.0 9.0 0.0 9.0 1.0 0.0 1.0 2.0 8.0 8.0
0.0 5.0 3.0 2.0 3.0 8.0 2.0 6.0 2.0 6.0
8.0 2.0 5.0 9.0 6.0 8.0 2.0 8.0 9.0 3.0
4.0 4.0 0.0 9.0 4.0 7.0 0.0 8.0 6.0 2.0
9.0 4.0 9.0 7.0 8.0 0.0 3.0 2.0 9.0 9.0


[matrices]multiplied =
351.0 257.0 222.0 352.0 286.0 173.0 150.0 172.0 384.0 280.0
257.0 290.0 187.0 299.0 262.0 158.0 121.0 148.0 304.0 272.0
222.0 187.0 271.0 224.0 276.0 178.0 119.0 146.0 303.0 280.0
352.0 299.0 224.0 423.0 298.0 192.0 127.0 231.0 415.0 293.0
286.0 262.0 276.0 298.0 365.0 236.0 168.0 174.0 342.0 291.0
173.0 158.0 178.0 192.0 236.0 331.0 107.0 222.0 257.0 211.0
150.0 121.0 119.0 127.0 168.0 107.0 121.0 61.0 152.0 130.0
172.0 148.0 146.0 231.0 174.0 222.0 61.0 209.0 250.0 184.0
384.0 304.0 303.0 415.0 342.0 257.0 152.0 250.0 497.0 358.0
280.0 272.0 280.0 293.0 291.0 211.0 130.0 184.0 358.0 384.0


[matrices]multiplied =
407.0 206.0 158.0 184.0 344.0 322.0 142.0 329.0 237.0 380.0
206.0 239.0 118.0 160.0 237.0 127.0 158.0 206.0 138.0 214.0
158.0 118.0 133.0 125.0 215.0 153.0 118.0 162.0 106.0 219.0
184.0 160.0 125.0 241.0 263.0 170.0 165.0 276.0 185.0 247.0
344.0 237.0 215.0 263.0 474.0 314.0 242.0 373.0 273.0 424.0
322.0 127.0 153.0 170.0 314.0 377.0 144.0 291.0 237.0 339.0
142.0 158.0 118.0 165.0 242.0 144.0 191.0 213.0 178.0 175.0
329.0 206.0 162.0 276.0 373.0 291.0 213.0 432.0 325.0 366.0
237.0 138.0 106.0 185.0 273.0 237.0 178.0 325.0 282.0 235.0
380.0 214.0 219.0 247.0 424.0 339.0 175.0 366.0 235.0 466.0


Eigenvectors =
0.9 0.6 0.5 0.6 1.0 0.8 0.5 1.0 0.7 1.0

Hermitian matrix =
1.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
-0.6 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
-0.5 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
-0.7 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0
-1.1 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0
-0.9 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0
-0.6 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0
-1.1 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0
-0.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0
-1.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0


[matrices]multiplied =
458.9 232.3 178.2 207.5 387.9 363.1 160.1 371.0 267.2 428.5
-53.3 107.8 17.3 42.8 17.9 -78.1 67.5 -3.6 -13.0 -28.1
-63.0 6.1 47.2 25.1 28.2 -21.9 40.9 -16.7 -22.7 12.6
-110.0 11.2 10.9 108.1 14.5 -62.6 62.4 38.3 13.8 -27.5
-123.7 0.3 33.5 51.6 78.7 -56.0 78.8 -5.0 0.7 -12.6
-49.5 -61.0 8.8 2.1 0.0 83.1 14.4 -9.3 20.7 -7.9
-105.1 33.0 22.1 53.3 33.2 -51.5 104.8 13.3 34.1 -55.7
-111.2 -16.8 -8.9 77.0 0.9 -57.3 59.4 76.2 68.7 -45.0
-87.1 -26.1 -19.8 38.5 -1.0 -19.4 64.9 63.0 93.3 -67.6
-78.9 -18.3 40.8 39.5 36.1 -24.1 14.9 -5.0 -32.2 37.5


Hermitian matrix inverse =
0.9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
-0.6 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
-0.5 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
-0.6 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0
-1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0
-0.8 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0
-0.5 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0
-1.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0
-0.7 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0
-1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0


[matrices]multiplied =
-1691.4 232.3 178.2 207.5 387.9 363.1 160.1 371.0 267.2 428.5
-94.5 107.8 17.3 42.8 17.9 -78.1 67.5 -3.6 -13.0 -28.1
-111.8 6.1 47.2 25.1 28.2 -21.9 40.9 -16.7 -22.7 12.6
-195.1 11.2 10.9 108.1 14.5 -62.6 62.4 38.3 13.8 -27.5
-219.3 0.3 33.5 51.6 78.7 -56.0 78.8 -5.0 0.7 -12.6
-87.8 -61.0 8.8 2.1 0.0 83.1 14.4 -9.3 20.7 -7.9
-186.3 33.0 22.1 53.3 33.2 -51.5 104.8 13.3 34.1 -55.7
-197.3 -16.8 -8.9 77.0 0.9 -57.3 59.4 76.2 68.7 -45.0
-154.5 -26.1 -19.8 38.5 -1.0 -19.4 64.9 63.0 93.3 -67.6
-140.0 -18.3 40.8 39.5 36.1 -24.1 14.9 -5.0 -32.2 37.5


Reduced matrix =
107.8 17.3 42.8 17.9 -78.1 67.5 -3.6 -13.0 -28.1
6.1 47.2 25.1 28.2 -21.9 40.9 -16.7 -22.7 12.6
11.2 10.9 108.1 14.5 -62.6 62.4 38.3 13.8 -27.5
0.3 33.5 51.6 78.7 -56.0 78.8 -5.0 0.7 -12.6
-61.0 8.8 2.1 0.0 83.1 14.4 -9.3 20.7 -7.9
33.0 22.1 53.3 33.2 -51.5 104.8 13.3 34.1 -55.7
-16.8 -8.9 77.0 0.9 -57.3 59.4 76.2 68.7 -45.0
-26.1 -19.8 38.5 -1.0 -19.4 64.9 63.0 93.3 -67.6
-18.3 40.8 39.5 36.1 -24.1 14.9 -5.0 -32.2 37.5


Eigenvectors =
3.2 1.3 3.7 3.1 -0.6 3.8 3.6 2.9 1.0

Hermitian matrix =
0.3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
-0.4 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
-1.1 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0
-1.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0
0.2 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0
-1.2 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0
-1.1 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0
-0.9 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0
-0.3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0


[matrices]multiplied =
33.2 5.3 13.2 5.5 -24.0 20.8 -1.1 -4.0 -8.6
-35.9 40.4 8.4 21.2 8.6 14.6 -15.3 -17.6 23.6
-110.8 -8.8 59.7 -5.7 25.8 -14.0 42.4 28.5 4.3
-103.9 16.7 10.2 61.5 19.6 13.5 -1.6 13.2 14.5
-39.8 12.2 10.5 3.5 67.7 27.7 -10.0 18.1 -13.4
-93.8 1.7 3.0 12.2 40.4 25.4 17.5 49.4 -22.6
-137.3 -28.3 29.2 -19.0 30.1 -16.1 80.2 83.2 -13.6
-120.8 -35.1 0.9 -16.6 49.2 5.6 66.1 104.7 -42.9
-51.4 35.5 26.4 30.6 -0.0 -5.9 -3.9 -28.2 46.2


Hermitian matrix inverse =
3.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
-1.3 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
-3.7 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0
-3.1 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0
0.6 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0
-3.8 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0
-3.6 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0
-2.9 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0
-1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0


[matrices]multiplied =
-35.4 5.3 13.2 5.5 -24.0 20.8 -1.1 -4.0 -8.6
-233.3 40.4 8.4 21.2 8.6 14.6 -15.3 -17.6 23.6
-720.1 -8.8 59.7 -5.7 25.8 -14.0 42.4 28.5 4.3
-675.3 16.7 10.2 61.5 19.6 13.5 -1.6 13.2 14.5
-258.9 12.2 10.5 3.5 67.7 27.7 -10.0 18.1 -13.4
-609.5 1.7 3.0 12.2 40.4 25.4 17.5 49.4 -22.6
-892.2 -28.3 29.2 -19.0 30.1 -16.1 80.2 83.2 -13.6
-785.0 -35.1 0.9 -16.6 49.2 5.6 66.1 104.7 -42.9
-334.3 35.5 26.4 30.6 -0.0 -5.9 -3.9 -28.2 46.2


Reduced matrix =
40.4 8.4 21.2 8.6 14.6 -15.3 -17.6 23.6
-8.8 59.7 -5.7 25.8 -14.0 42.4 28.5 4.3
16.7 10.2 61.5 19.6 13.5 -1.6 13.2 14.5
12.2 10.5 3.5 67.7 27.7 -10.0 18.1 -13.4
1.7 3.0 12.2 40.4 25.4 17.5 49.4 -22.6
-28.3 29.2 -19.0 30.1 -16.1 80.2 83.2 -13.6
-35.1 0.9 -16.6 49.2 5.6 66.1 104.7 -42.9
35.5 26.4 30.6 -0.0 -5.9 -3.9 -28.2 46.2


Eigenvectors =
0.8 -3.8 -1.5 -1.8 -3.7 -6.8 -7.4 1.0

Hermitian matrix =
1.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0
4.5 1.0 0.0 0.0 0.0 0.0 0.0 0.0
1.7 0.0 1.0 0.0 0.0 0.0 0.0 0.0
2.1 0.0 0.0 1.0 0.0 0.0 0.0 0.0
4.4 0.0 0.0 0.0 1.0 0.0 0.0 0.0
8.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0
8.7 0.0 0.0 0.0 0.0 0.0 1.0 0.0
-1.2 0.0 0.0 0.0 0.0 0.0 0.0 1.0


[matrices]multiplied =
47.9 9.9 25.1 10.2 17.2 -18.1 -20.9 27.9
173.3 97.5 89.9 64.6 51.5 -26.3 -51.0 110.5
86.2 24.6 97.9 34.3 38.5 -27.8 -17.1 55.1
98.9 28.5 49.0 86.2 58.9 -42.7 -19.7 37.2
180.6 40.1 106.1 78.5 89.7 -50.0 -28.7 81.7
296.1 96.5 151.2 99.0 100.6 -42.3 -58.4 175.6
317.3 74.0 168.3 124.2 132.3 -66.9 -49.1 162.6
-12.4 16.4 5.5 -10.2 -23.1 14.2 -7.3 18.2


Hermitian matrix inverse =
0.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0
3.8 1.0 0.0 0.0 0.0 0.0 0.0 0.0
1.5 0.0 1.0 0.0 0.0 0.0 0.0 0.0
1.8 0.0 0.0 1.0 0.0 0.0 0.0 0.0
3.7 0.0 0.0 0.0 1.0 0.0 0.0 0.0
6.8 0.0 0.0 0.0 0.0 1.0 0.0 0.0
7.4 0.0 0.0 0.0 0.0 0.0 1.0 0.0
-1.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0


[matrices]multiplied =
-106.6 9.9 25.1 10.2 17.2 -18.1 -20.9 27.9
292.7 97.5 89.9 64.6 51.5 -26.3 -51.0 110.5
145.5 24.6 97.9 34.3 38.5 -27.8 -17.1 55.1
167.0 28.5 49.0 86.2 58.9 -42.7 -19.7 37.2
305.0 40.1 106.1 78.5 89.7 -50.0 -28.7 81.7
500.0 96.5 151.2 99.0 100.6 -42.3 -58.4 175.6
535.9 74.0 168.3 124.2 132.3 -66.9 -49.1 162.6
-20.9 16.4 5.5 -10.2 -23.1 14.2 -7.3 18.2


Reduced matrix =
97.5 89.9 64.6 51.5 -26.3 -51.0 110.5
24.6 97.9 34.3 38.5 -27.8 -17.1 55.1
28.5 49.0 86.2 58.9 -42.7 -19.7 37.2
40.1 106.1 78.5 89.7 -50.0 -28.7 81.7
96.5 151.2 99.0 100.6 -42.3 -58.4 175.6
74.0 168.3 124.2 132.3 -66.9 -49.1 162.6
16.4 5.5 -10.2 -23.1 14.2 -7.3 18.2


Eigenvectors =
45.4 27.6 25.3 43.8 72.1 75.5 1.0

Hermitian matrix =
0.0 0.0 0.0 0.0 0.0 0.0 0.0
-0.6 1.0 0.0 0.0 0.0 0.0 0.0
-0.6 0.0 1.0 0.0 0.0 0.0 0.0
-1.0 0.0 0.0 1.0 0.0 0.0 0.0
-1.6 0.0 0.0 0.0 1.0 0.0 0.0
-1.7 0.0 0.0 0.0 0.0 1.0 0.0
-0.0 0.0 0.0 0.0 0.0 0.0 1.0


[matrices]multiplied =
2.1 2.0 1.4 1.1 -0.6 -1.1 2.4
-34.7 43.2 -5.0 7.2 -11.8 13.9 -12.2
-25.8 -1.0 50.2 30.2 -28.1 8.7 -24.3
-54.0 19.3 16.1 40.0 -24.6 20.6 -25.0
-58.2 8.5 -3.5 18.9 -0.5 22.5 0.1
-88.1 18.8 16.8 46.7 -23.1 35.7 -21.2
14.3 3.5 -11.6 -24.3 14.8 -6.2 15.8


Hermitian matrix inverse =
45.4 0.0 0.0 0.0 0.0 0.0 0.0
-27.6 1.0 0.0 0.0 0.0 0.0 0.0
-25.3 0.0 1.0 0.0 0.0 0.0 0.0
-43.8 0.0 0.0 1.0 0.0 0.0 0.0
-72.1 0.0 0.0 0.0 1.0 0.0 0.0
-75.5 0.0 0.0 0.0 0.0 1.0 0.0
-1.0 0.0 0.0 0.0 0.0 0.0 1.0


[matrices]multiplied =
81.2 2.0 1.4 1.1 -0.6 -1.1 2.4
-3151.5 43.2 -5.0 7.2 -11.8 13.9 -12.2
-2341.1 -1.0 50.2 30.2 -28.1 8.7 -24.3
-4899.1 19.3 16.1 40.0 -24.6 20.6 -25.0
-5285.4 8.5 -3.5 18.9 -0.5 22.5 0.1
-7997.8 18.8 16.8 46.7 -23.1 35.7 -21.2
1295.9 3.5 -11.6 -24.3 14.8 -6.2 15.8


Reduced matrix =
43.2 -5.0 7.2 -11.8 13.9 -12.2
-1.0 50.2 30.2 -28.1 8.7 -24.3
19.3 16.1 40.0 -24.6 20.6 -25.0
8.5 -3.5 18.9 -0.5 22.5 0.1
18.8 16.8 46.7 -23.1 35.7 -21.2
3.5 -11.6 -24.3 14.8 -6.2 15.8


Eigenvectors =
-0.9 -2.1 -2.1 -1.2 -2.8 1.0

Hermitian matrix =
-1.1 0.0 0.0 0.0 0.0 0.0
-2.2 1.0 0.0 0.0 0.0 0.0
-2.3 0.0 1.0 0.0 0.0 0.0
-1.2 0.0 0.0 1.0 0.0 0.0
-3.0 0.0 0.0 0.0 1.0 0.0
1.1 0.0 0.0 0.0 0.0 1.0


[matrices]multiplied =
-46.5 5.4 -7.7 12.7 -15.0 13.2
-97.2 61.3 14.2 -1.9 -22.4 2.9
-80.6 27.6 23.4 2.6 -11.7 3.3
-45.4 2.8 9.9 14.2 5.1 15.4
-110.0 31.6 25.3 12.0 -5.9 15.3
50.0 -17.0 -16.5 2.1 8.8 2.6


Hermitian matrix inverse =
-0.9 0.0 0.0 0.0 0.0 0.0
2.1 1.0 0.0 0.0 0.0 0.0
2.1 0.0 1.0 0.0 0.0 0.0
1.2 0.0 0.0 1.0 0.0 0.0
2.8 0.0 0.0 0.0 1.0 0.0
-1.0 0.0 0.0 0.0 0.0 1.0


[matrices]multiplied =
-2.3 5.4 -7.7 12.7 -15.0 13.2
180.5 61.3 14.2 -1.9 -22.4 2.9
149.7 27.6 23.4 2.6 -11.7 3.3
84.4 2.8 9.9 14.2 5.1 15.4
204.2 31.6 25.3 12.0 -5.9 15.3
-92.9 -17.0 -16.5 2.1 8.8 2.6


Reduced matrix =
61.3 14.2 -1.9 -22.4 2.9
27.6 23.4 2.6 -11.7 3.3
2.8 9.9 14.2 5.1 15.4
31.6 25.3 12.0 -5.9 15.3
-17.0 -16.5 2.1 8.8 2.6


Eigenvectors =
-2.4 -1.5 -0.4 -1.8 1.0

Hermitian matrix =
-0.4 0.0 0.0 0.0 0.0
-0.6 1.0 0.0 0.0 0.0
-0.2 0.0 1.0 0.0 0.0
-0.7 0.0 0.0 1.0 0.0
0.4 0.0 0.0 0.0 1.0


[matrices]multiplied =
-25.4 -5.9 0.8 9.3 -1.2
-11.0 14.5 3.8 2.4 1.5
-7.7 7.5 14.5 8.9 14.9
-14.2 14.7 13.4 10.9 13.1
8.4 -10.6 1.3 -0.5 3.8


Hermitian matrix inverse =
-2.4 0.0 0.0 0.0 0.0
1.5 1.0 0.0 0.0 0.0
0.4 0.0 1.0 0.0 0.0
1.8 0.0 0.0 1.0 0.0
-1.0 0.0 0.0 0.0 1.0


[matrices]multiplied =
70.6 -5.9 0.8 9.3 -1.2
52.8 14.5 3.8 2.4 1.5
36.9 7.5 14.5 8.9 14.9
68.6 14.7 13.4 10.9 13.1
-40.6 -10.6 1.3 -0.5 3.8


Reduced matrix =
14.5 3.8 2.4 1.5
7.5 14.5 8.9 14.9
14.7 13.4 10.9 13.1
-10.6 1.3 -0.5 3.8


Eigenvectors =
-2.4 -4.4 -5.3 1.0

Hermitian matrix =
-0.4 0.0 0.0 0.0
-1.8 1.0 0.0 0.0
-2.2 0.0 1.0 0.0
0.4 0.0 0.0 1.0


[matrices]multiplied =
-6.0 -1.6 -1.0 -0.6
-18.8 7.6 4.6 12.3
-17.3 5.0 5.6 9.9
-4.6 2.9 0.5 4.4


Hermitian matrix inverse =
-2.4 0.0 0.0 0.0
4.4 1.0 0.0 0.0
5.3 0.0 1.0 0.0
-1.0 0.0 0.0 1.0


[matrices]multiplied =
2.9 -1.6 -1.0 -0.6
90.3 7.6 4.6 12.3
82.9 5.0 5.6 9.9
22.1 2.9 0.5 4.4


Reduced matrix =
7.6 4.6 12.3
5.0 5.6 9.9
2.9 0.5 4.4


Eigenvectors =
3.2 2.7 1.0

Hermitian matrix =
0.3 0.0 0.0
-0.8 1.0 0.0
-0.3 0.0 1.0


[matrices]multiplied =
2.4 1.4 3.8
-1.4 1.8 -0.4
0.6 -0.9 0.6


Hermitian matrix inverse =
3.2 0.0 0.0
-2.7 1.0 0.0
-1.0 0.0 1.0


[matrices]multiplied =
0.0 1.4 3.8
-8.7 1.8 -0.4
3.6 -0.9 0.6


Reduced matrix =
1.8 -0.4
-0.9 0.6


Eigenvectors =
-1.6 1.0

Hermitian matrix =
-0.6 0.0
0.6 1.0


[matrices]multiplied =
-1.1 0.3
0.2 0.4


Hermitian matrix inverse =
-1.6 0.0
-1.0 1.0


[matrices]multiplied =
1.5 0.3
-0.7 0.4


Reduced matrix =
0.4


Eigenvectors =
0.9 0.6 0.5 0.6 1.0 0.8 0.5 1.0 0.7 1.0

Eigenvectors =
1.4 -1.1 -0.0 -1.2 -0.3 1.7 -1.5 -0.7 -0.6 1.0

Eigenvectors =
0.2 1.4 0.9 -0.0 0.8 -0.9 0.0 -1.2 -1.8 1.0

Eigenvectors =
-3.1 -3.2 1.6 0.9 1.9 1.2 0.8 -0.8 -0.6 1.0

Eigenvectors =
0.0 -0.6 -0.2 1.2 -0.4 -1.1 -1.3 1.0 -0.5 1.0

Eigenvectors =
1.7 -3.8 -1.4 -7.9 8.1 -7.7 -0.9 1.5 3.4 1.0

Eigenvectors =
-0.6 0.1 2.3 -1.5 -1.8 -0.5 0.4 0.9 0.6 1.0

Eigenvectors =
-2.3 1.8 -1.3 -1.0 0.5 1.0 -1.4 0.6 0.3 1.0

Eigenvectors =
0.0 -0.8 -2.6 -1.5 -0.6 0.5 3.4 2.7 -3.6 1.0

Eigenvectors =
-0.0 -0.1 -0.6 0.1 -0.4 -0.3 0.5 -0.8 0.6 1.0

[matrix]transposed =
0.4 0.4 0.1 -0.6 0.0 0.1 -0.2 -0.6 0.0 -0.0
0.2 -0.3 0.4 -0.6 -0.2 -0.3 0.0 0.4 -0.1 -0.1
0.2 -0.0 0.3 0.3 -0.1 -0.1 0.6 -0.3 -0.4 -0.4
0.3 -0.4 -0.0 0.2 0.4 -0.5 -0.4 -0.3 -0.2 0.1
0.4 -0.1 0.3 0.3 -0.2 0.5 -0.5 0.1 -0.1 -0.3
0.3 0.5 -0.3 0.2 -0.4 -0.5 -0.1 0.2 0.1 -0.1
0.2 -0.4 0.0 0.1 -0.5 -0.1 0.1 -0.4 0.5 0.3
0.4 -0.2 -0.4 -0.1 0.4 0.1 0.3 0.2 0.4 -0.5
0.3 -0.2 -0.6 -0.1 -0.2 0.2 0.2 0.1 -0.5 0.4
0.4 0.3 0.3 0.2 0.4 0.1 0.3 0.3 0.2 0.6


inverse diagonal matrix =
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.1 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.1 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.1 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.2 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.3 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.7 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.6


[matrices]multiplied =
17.2 5.0 -1.6 -2.4 2.4 -3.1 1.0 1.8 0.6 0.0
15.0 3.6 0.5 -0.8 -6.8 0.5 -2.1 -0.5 0.5 0.0
14.3 -1.6 6.1 2.7 3.6 2.4 0.1 -0.8 0.7 -0.2
18.8 5.0 -6.1 -0.6 -0.7 2.1 1.8 -0.4 -0.4 -0.3
17.4 -1.5 5.1 -4.6 -0.1 3.5 0.2 1.4 -0.4 0.2
13.0 -12.2 -2.1 -1.9 -1.1 -1.7 -0.8 0.7 -0.0 -0.2
8.0 -0.0 3.7 -5.2 0.3 -2.9 1.1 -2.6 -0.2 0.0
11.6 -5.5 -6.0 1.8 -0.2 1.4 1.7 -1.0 0.4 0.3
21.4 1.7 -2.7 1.9 3.9 -0.8 -3.2 -0.7 -0.4 0.1
17.4 -0.1 4.8 6.4 -2.7 -2.4 1.5 0.5 -0.4 0.0


[matrices]multiplied =
0.3 0.3 -0.1 -0.2 0.3 -0.4 0.2 0.5 0.4 0.1
0.3 0.2 0.0 -0.1 -0.7 0.1 -0.4 -0.1 0.4 0.0
0.3 -0.1 0.4 0.3 0.4 0.3 0.0 -0.2 0.5 -0.4
0.4 0.3 -0.4 -0.1 -0.1 0.3 0.3 -0.1 -0.3 -0.5
0.3 -0.1 0.4 -0.4 -0.0 0.5 0.0 0.3 -0.3 0.3
0.3 -0.8 -0.2 -0.2 -0.1 -0.2 -0.2 0.2 -0.0 -0.4
0.2 -0.0 0.3 -0.5 0.0 -0.4 0.2 -0.7 -0.1 0.0
0.2 -0.3 -0.4 0.2 -0.0 0.2 0.3 -0.3 0.3 0.6
0.4 0.1 -0.2 0.2 0.4 -0.1 -0.6 -0.2 -0.3 0.2
0.3 -0.0 0.4 0.6 -0.3 -0.3 0.3 0.1 -0.3 0.1


S =
50.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 15.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 13.7 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 10.7 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 9.4 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 7.2 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 5.1 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.9 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.4 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.6


U =
0.3 0.3 -0.1 -0.2 0.3 -0.4 0.2 0.5 0.4 0.1
0.3 0.2 0.0 -0.1 -0.7 0.1 -0.4 -0.1 0.4 0.0
0.3 -0.1 0.4 0.3 0.4 0.3 0.0 -0.2 0.5 -0.4
0.4 0.3 -0.4 -0.1 -0.1 0.3 0.3 -0.1 -0.3 -0.5
0.3 -0.1 0.4 -0.4 -0.0 0.5 0.0 0.3 -0.3 0.3
0.3 -0.8 -0.2 -0.2 -0.1 -0.2 -0.2 0.2 -0.0 -0.4
0.2 -0.0 0.3 -0.5 0.0 -0.4 0.2 -0.7 -0.1 0.0
0.2 -0.3 -0.4 0.2 -0.0 0.2 0.3 -0.3 0.3 0.6
0.4 0.1 -0.2 0.2 0.4 -0.1 -0.6 -0.2 -0.3 0.2
0.3 -0.0 0.4 0.6 -0.3 -0.3 0.3 0.1 -0.3 0.1


V =
0.4 0.4 0.1 -0.6 0.0 0.1 -0.2 -0.6 0.0 -0.0
0.2 -0.3 0.4 -0.6 -0.2 -0.3 0.0 0.4 -0.1 -0.1
0.2 -0.0 0.3 0.3 -0.1 -0.1 0.6 -0.3 -0.4 -0.4
0.3 -0.4 -0.0 0.2 0.4 -0.5 -0.4 -0.3 -0.2 0.1
0.4 -0.1 0.3 0.3 -0.2 0.5 -0.5 0.1 -0.1 -0.3
0.3 0.5 -0.3 0.2 -0.4 -0.5 -0.1 0.2 0.1 -0.1
0.2 -0.4 0.0 0.1 -0.5 -0.1 0.1 -0.4 0.5 0.3
0.4 -0.2 -0.4 -0.1 0.4 0.1 0.3 0.2 0.4 -0.5
0.3 -0.2 -0.6 -0.1 -0.2 0.2 0.2 0.1 -0.5 0.4
0.4 0.3 0.3 0.2 0.4 0.1 0.3 0.3 0.2 0.6


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