Hello I am trying to determine wether a given matrix is symmetric and
positive matrix. The matrix has real valued elements.
I have been reading about the cholesky method and another method is to find
the eigenvalues. I cant understand how to implement either of the two. Can
someone point me to the right direction. I have used ?chol to see the help
but if the matrix is not positive definite it comes up as error. I know how
to the get the eigenvalues but how can I then put this into a program to
check them as the just come up with $values.
Is checking that the eigenvalues are positive enough to determine wether the
matrix is positive definite?
m
[,1] [,2] [,3] [,4] [,5]
[1,] 1.0 0.0 0.5 -0.3 0.2
[2,] 0.0 1.0 0.1 0.0 0.0
[3,] 0.5 0.1 1.0 0.3 0.7
[4,] -0.3 0.0 0.3 1.0 0.4
[5,] 0.2 0.0 0.7 0.4 1.0
this is the matrix that I know is positive definite.
eigen(m)
$values
[1] 2.0654025 1.3391291 1.0027378 0.3956079 0.1971228
$vectors
[,1] [,2] [,3] [,4] [,5]
[1,] -0.32843233 0.69840166 0.080549876 0.44379474 0.44824689
[2,] -0.06080335 0.03564769 -0.993062427 -0.01474690 0.09296096
[3,] -0.64780034 0.12089168 -0.027187620 0.08912912 -0.74636235
[4,] -0.31765040 -0.68827876 0.007856812 0.60775962 0.23651023
[5,] -0.60653780 -0.15040584 0.080856897 -0.65231358 0.42123526
and this are the eigenvalues and eigenvectors.
I thought of using
eigen(m,only.values=T)
$values
[1] 2.0654025 1.3391291 1.0027378 0.3956079 0.1971228
$vectors
NULL
Then i thought of using logical expression to determine if there are
negative eigenvalues but couldnt work. I dont know what error this is
b<-(a<0)
Error: (list) object cannot be coerced to type 'double'
Thanks
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