  Consider a standard white Wishart matrix with parameters $n$ and $p$.
Motivated by applications in high-dimensional statistics and signal processing,
we perform asymptotic analysis on the maxima and minima of the eigenvalues of
all the $m \times m$ principal minors, under the asymptotic regime that $n,p,m$
go to infinity. Asymptotic results concerning extreme eigenvalues of principal
minors of real Wigner matrices are also obtained. In addition, we discuss an
application of the theoretical results to the construction of compressed
sensing matrices, which provides insights to compressed sensing in signal
processing and high dimensional linear regression in statistics.
