Proposition 1. Let X be a Banach space, M a closed subspace of X, and X/M the quotient space with the quotient norm defined as above. Then X/M is also a Banach space. (查看原文)
Since the solution to the approximation problem is equivalent to solution to the normal equations, it is clear that the Gram-Schmidt procedure can be interpreted as a procedure for inverting the Gram matrix. Conversely, many effective algorithms for solving the normal equations have an interpretation in terms of the minimum norm problem in Hilbert space. (p. 63) (查看原文)
