  In this paper, within a unified framework of the condition number theory we
present the explicit expression of the projected condition number of the
equality constrained indefinite least squares problem. By setting specific
norms and parameters, some widely used condition numbers, like the normwise,
mixed and componentwise condition numbers follow as its special cases.
Considering practical applications and computation, some new compact forms or
upper bounds of the projected condition numbers are given to improve the
computational efficiency. The new compact forms are of particular interest in
calculating the exact value of the 2-norm projected condition numbers. When the
equality constrained indefinite least squares problem degenerates into some
specific least squares problems, our results give some new findings on the
condition number theory of these specific least squares problems. Numerical
experiments are given to illustrate our theoretical results.
