  We describe noncommutative desingularizations of determinantal varieties,
determinantal varieties defined by minors of generic symmetric matrices, and
pfaffian varieties defined by pfaffians of generic anti-symmetric matrices. For
maximal minors of square matrices and symmetric matrices, this gives a
non-commutative crepant resolution. Along the way, we describe a method to
calculate the quiver with relations for any non-commutative desingularizations
coming from exceptional collections over partial flag varieties.
