  Driessel ["Computing canonical forms using flows", Linear Algebra and Its
Applications 2004] introduced the notion of quasi-projection onto the range of
a linear transformation from one inner product space into another inner product
space. Here we introduce the notion of quasi-projection onto the intersection
of the ranges of two linear transformations from two inner product spaces into
a third inner product space. As an application, we design a new family of
iso-spectral flows on the space of symmetric matrices that preserves zero
patterns. We discuss the equilibrium points of these flows. We conjecture that
these flows generically converge to diagonal matrices. We perform some
numerical experiments with these flows which support this conjecture. We also
compare our zero preserving flows with the Toda flow.
