System Is Computationally Singular: Reciprocal Condition Number in R

System is computationally singular: reciprocal condition number in R

Two fundamental linear algebra properties:

1. A singular (square) matrix is a (square) matrix that is not invertible.
2. A matrix is not invertible if its determinant equals zero.

If you check

set.seed(2018);
x <- matrix(rnorm(80, mean = 0, sd = 0.1), 8, 8)
c <- cov(x)
det(c)
#[1] -3.109158e-38

So indeed, det(c) is zero (within machine precision); hence c is not invertible, which is exactly what solve(c) is trying to do.

PS 1: Take a look at ?solve to see that solve(a) will return the inverse of a.

PS 2: There exists a nice post on Mathematics on the interpretation of the determinant of the covariance matrix. Take a look to understand why you're seeing what you're seeing.

Error system is computationally singular when trying to run panel data regression

Changing the unit as a workaround solved the problem.

Mahalonobis distance in R, error: system is computationally singular

The Mahalanobis distance requires you to calculate the inverse of the covariance matrix. The function mahalanobis internally uses solve which is a numerical way to calculate the inverse. Unfortunately, if some of the numbers used in the inverse calculation are very small, it assumes that they are zero, leading to the assumption that it is a singular matrix. This is why it specifies that they are computationally singular, because the matrix might not be singular given a different tolerance.

The solution is to set the tolerance for when it assumes that they are zero. Fortunately, mahalanobis allows you to pass this parameter (tol) to solve:

mahalanobis(dat,center=centroid,cov=cov(dat),tol=1e-20)
# [1] 24.215494 28.394913  6.984101 28.004975 11.095357 14.401967 ...

Can you use a reciprocal condition when getting Error in solve.default when using svychisq

Thank you so much for the answers. After running the table I realized the issue was that the responses weren't evenly distributed. So, I recoded the outcomes to only those I wanted, throwing the rest into an "other" category and that worked!

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