Volume 18, Number 1, Spring 2010
EXPANSIONS FOR FUNCTIONS OF
DETERMINANTS OF POWER SERIES
CHRISTOPHER S. WITHERS AND SARALEES NADARAJAH
Abstract. Let A (ε) be an analytic n x n matrix function
of a scalar ε. We obtain expansions in powers of ε for det A (ε)
and smooth functions of it including its powers and its log. An
application is given to multivariate statistics.