Re: Condition on singular or nearly singular correlation matrices

mzhang33@xxxxxxxxx wrote:
Hi there,

I heard that there is a theorem saying that for a correlation matrix,
if all the off diaganol elements are very small, then it cannot be
nearly singular. The only way to make it nearly singular is to increase
all the off diaganol elements to values close to 1. However I failed to
find the name of the therom. Does anyone know it? Any reference?
Thanks!

Mike

A p-variable correlation matrix will be singular if the average
correlation is -1/(p-1), which will be close to zero if p is large.

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