Hi Cleber,
there is no hard-and-fast "magic number" here. Ill-conditioning also
depends on what you are trying to do (inference? prediction?). The
condition number is only one of a number of conditioning/collinearity
diagnostics commonly used. Take a look at:
Golub, G. H., & Van Loan, C. F. (1996). Matrix Computations (3rd ed.).
Baltimore: Johns Hopkins University Press.
Belsley, D. A. (1991a). Conditioning Diagnostics: Collinearity and Weak
Data in Regression. New York, NY: Wiley.
Hill, R. C., & Adkins, L. C. (2001). Collinearity. In B. H. Baltagi
(Ed.), A Companion to Theoretical Econometrics (p. 256-278). Oxford:
Blackwell
HTH,
Stephan
Cleber Nogueira Borges schrieb:
Hello,
is there a upper limit to kappa value where I can consider a matrix
well-conditioned?
Cleber
Kingsford Jones wrote:
I suppose the solution is unstable because x is ill-conditioned:
x
[,1] [,2] [,3] [,4]
[1,] 0.133 0.254 -0.214 0.116
[2,] 0.254 0.623 -0.674 0.139
[3,] -0.214 -0.674 0.910 0.011
[4,] 0.116 0.139 0.011 0.180
cor(x)
[,1] [,2] [,3] [,4]
[1,] 1.0000000 0.9963557 -0.9883690 0.8548065
[2,] 0.9963557 1.0000000 -0.9976663 0.8084090
[3,] -0.9883690 -0.9976663 1.0000000 -0.7663847
[4,] 0.8548065 0.8084090 -0.7663847 1.0000000
kappa(x)
[1] 2813.326
hth,
Kingsford Jones
On Thu, Jan 29, 2009 at 7:00 PM, Joseph P Gray <jpg...@uwm.edu> wrote:
I submit the following matrix to both MATLAB and R
x= 0.133 0.254 -0.214 0.116
0.254 0.623 -0.674 0.139
-0.214 -0.674 0.910 0.011
0.116 0.139 0.011 0.180
MATLAB's inv(x) provides the following
137.21 -50.68 -4.70 -46.42
-120.71 27.28 -8.94 62.19
-58.15 6.93 -7.89 36.94
8.35 11.17 10.42 -14.82
R's solve(x) provides:
261.94 116.22 150.92 -267.78
116.22 344.30 286.68 -358.30
150.92 286.68 252.96 -334.09
-267.78 =358.30 -334.09 475.22
inv(x)*x = I(4)
and solve(x)%*%x = I(4)
Is there a way to obtain the MATLAB result in R?
Thanks for any help.
Pat Gray
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