Condition on singular or nearly singular correlation matrices

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

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