A Matrix Inequality
Robert K. Meany · SIAM Journal on Numerical Analysis · 1969
If y is perpendicular to xi, (I xixT)y = y, while (I xixT)xi = 0. Thus (I xix') projects an arbitrary vector y onto the hyperplane perpendicular to xi, and A corresponds to a sequence of projections. The matrix A arises in an algorithm which the author has studied [1], and Theorem 1 shows how the rate of convergence of this algorithm, for the case k < n, is related to det XTX. An interpretation of det XTX is discussed in ? 2.