 Posted Saturday, May 02, 2009 7:27 PM
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I submitted a matrix which I will give below. The trace was given as zero, the eigenvalues, when I added them up, summed to 1. I thought they should sum to zero (the trace). Can you explain what's happening?
Here is matrix I entered:
0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0
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Posted Sunday, May 03, 2009 12:21 PM
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| Hello, I have checked the result and the eigenvalues sum to zero, which is the same as the trace. Please verify the result again.
Trifon Triantafillidis | Lead Developer | 
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Posted Sunday, May 03, 2009 1:49 PM
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I did this again and the eigenvalues I get are:
igenvalues:
( 4, 0i)
( 3, 0i)
(-1, 0i)
( 0, 0i)
( 0, 0i)
( 3, 0i)
( 3, 0i)
( 3, 0i)
(-2, 0i)
(-2, 0i)
(-2, 0i)
( 0, 0i)
(-1, 0i)
(-1, 0i)
(-1, 0i)
(-1, 0i)
(-1, 0i)
(-1, 0i)
(-1, 0i)
(-1, 0i)
when I add this up it sums to one--there is positive four and three with multiplicity four, which gives sixteen; the negative eigenvalues are -2 (multiplicity three) and -1 (multiplicity 9) for a total of -15 -- and three times zero, which doesn't affect the sum. Please explain.
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Posted Monday, May 04, 2009 11:02 AM
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| That's funny, for the above matrix I get the following eigenvalues: ( 3.588, 0.000i)
( 2.594, 0.000i)
(-1.182, 0.000i)
(-0.172, 0.000i)
(-0.172, 0.000i)
( 3.064, 0.000i)
( 3.064, 0.000i)
( 3.064, 0.000i)
(-1.892, 0.000i)
(-1.892, 0.000i)
(-1.892, 0.000i)
(-0.172, 0.000i)
(-1.000, 0.000i)
(-1.000, 0.000i)
(-1.000, 0.000i)
(-1.000, 0.000i)
(-1.000, 0.000i)
(-1.000, 0.000i)
(-1.000, 0.000i)
(-1.000, 0.000i) which they do sum to zero.
Trifon Triantafillidis | Lead Developer | |
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Posted Monday, May 04, 2009 11:05 AM
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| Oh, I think I got it! It seems that you you setting "Show results using ... digits to" to 0 therefore the eigenvalues are rounded to the nearest whole number. Is that so?
Trifon Triantafillidis | Lead Developer | |
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Posted Monday, May 04, 2009 2:46 PM
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| yes -- had set digits to zero -- thanks for pointing it out. Thanks.
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