  This paper introduces a novel two-sample test for a broad class of
orthogonally equivalent positive definite symmetric matrix distributions. Our
test is the first of its kind and we derive its asymptotic distribution. To
estimate the test power, we use a warp-speed bootstrap method and consider the
most common matrix distributions. We provide several real data examples,
including the data for main cryptocurrencies and stock data of major US
companies. The real data examples demonstrate the applicability of our test in
the context closely related to algorithmic trading. The popularity of matrix
distributions in many applications and the need for such a test in the
literature are reconciled by our findings.
