In
a linear differential algebraic equation with properly stated leading term,
the involved derivatives of the unknown function are figured out by an
additional matrix coefficient being in some sense well matched with the
leading coefficient matrix. Supposed all matrix coefficients are continuous,
for these equations, the notion of regularity with index $\mu$ is introduced
via a certain matrix sequence built up from the coefficient matrices and
then proved to be invariant under regular transformations. The Kronecker
index, the global index, and the tractability index for standard form differential
algebraic equations are covered as well. Moreover, inherent regular ordinary
differential equations that govern the dynamics are described in detail
and it is shown that transformations applied to them are closely related
to refactorizations of the leading term in the original equation.
**Keywords: ***differential
algebraic equations, regularity, index*