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RE: trace - sum of eigenvalues

monclerjacketsdxq — Mon, 10 Oct 2011 02:42:18 GMT

good post

RE: trace - sum of eigenvalues

Cementox — Mon, 06 Jun 2011 06:51:32 GMT

This site looks like it's gonna be very helpful for people.

RE: trace - sum of eigenvalues

chrisnyc — Mon, 04 May 2009 14:46:14 GMT

yes -- had set digits to zero -- thanks for pointing it out. Thanks.

RE: trace - sum of eigenvalues

Trifon — Mon, 04 May 2009 11:05:57 GMT

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?

RE: trace - sum of eigenvalues

Trifon — Mon, 04 May 2009 11:02:29 GMT

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.

RE: trace - sum of eigenvalues

chrisnyc — Sun, 03 May 2009 13:49:33 GMT

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.

RE: trace - sum of eigenvalues

Trifon — Sun, 03 May 2009 12:21:53 GMT

Hello,

I have checked the result and the eigenvalues sum to zero, which is the same as the trace. Please verify the result again.

trace - sum of eigenvalues

chrisnyc — Sat, 02 May 2009 19:27:11 GMT

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