# Question:Eingenvalues with Digits>15

## Question:Eingenvalues with Digits>15

Hi guys,

I've a bad 6x6 matrix, which contains both very big (10^14) and very small (~10) numbers, so that the inversion with digits=15 is pretty bad (if I multiply the inverse by the original one I've offdiagonal elements of the order of 10^6!!!).

I was trying to calculate the Eigenvalues, but something strange happens. With Digits=15

Eigenvalues=  ﻿﻿Vector(6, {(1) = -0.2101e-1, (2) = .83693, (3) = 114.86139, (4) = 19791.80546, (5) = 134594000.00000, (6) = 624049000000000.})

and

Determinant: -1.08101*10^17

But if I try Digits>16 (ie over the hardware precision, I think):

Eigenvalues: Error, (in HWcall) Segmentation Violation occurred in external routine

while the determinant is oscillating:

Determinant:

Dig=16 --> 5.79161*10^17
Dig =17--> -7.08275*10^16
Dig=20 --> 1.65365 *10^13
Dig=30 --> 5398.61244,
and for Dig>~40 --> 0.0000

Do you know what's happening????

The matrix is:

Matrix(6, 6, {(1, 1) = 156393396.533701532179918215869026476966, (1, 2) = -118243903475.827285569404582605530765663, (1, 3) = -6263333.73617023234383582644338323627622, (1, 4) = -185091.483826089501251512713737005555751, (1, 5) = 80790.9801929789813449825471731605781843, (1, 6) = 1086348.92359099037490942739843407023680, (2, 2) = 624048841842745.066305236557017731156085, (2, 3) = -14223324279.9671059208805631179717784309, (2, 4) = 271390990.212364081029432696123806175245, (2, 5) = -6789557.78040918751895574011616954335163, (2, 6) = -887211297.790616808899440297249969343478, (3, 3) = 942997.103500826358338353949909438447968, (3, 4) = 2390.98882773656471330090678451501720186, (3, 5) = -5202.67399895018046545215520415279523662, (3, 6) = -41059.7545428613547434057144743597172361, (4, 4) = 258.746505379263550904147446064209326068, (4, 5) = -80.0681808327239671077263126470862610300, (4, 6) = -1305.03399424659072471164804998119366346, (5, 5) = 128.203084138681407601505798776377859168, (5, 6) = 501.829272012377495290246242165653330606, (6, 6) = 7588.85431135042280667483054584887636828}, storage = triangular[upper], shape = [symmetric]) ;

The problem with the oscillating determinant disappear if one consideres the submatrix [1..-2,1..-2].

Thanks

S.

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