  I show analytically that the average of $k$ bootstrapped correlation matrices
rapidly becomes positive-definite as $k$ increases, which provides a simple
approach to regularize singular Pearson correlation matrices. If $n$ is the
number of objects and $t$ the number of features, the averaged correlation
matrix is almost surely positive-definite if $k> \frac{e}{e-1}\frac{n}{t}\simeq
1.58\frac{n}{t}$ in the limit of large $t$ and $n$. The probability of
obtaining a positive-definite correlation matrix with $k$ bootstraps is also
derived for finite $n$ and $t$. Finally, I demonstrate that the number of
required bootstraps is always smaller than $n$. This method is particularly
relevant in fields where $n$ is orders of magnitude larger than the size of
data points $t$, e.g., in finance, genetics, social science, or image
processing.
