Book-review by Ioan URSU. WHY DAVID HILBERT? Methods of Mathematical Physics, vol. 1 (575 pp, April 1989) Methods of Mathematical Physics, vol. 2, Differential Equations (852 pages, April 1989), by Richard Courant and David Hilbert ? WILEY-VCH

摘要

h space, a Hilbert space is an abstract (complete) normed vector space possessing the structure of an inner product that allows length and angle to be measured. Here the formalist Hilbert introduced a very intuitive concept. Exact analogs of the Pythagorean theorem and parallelogram law hold in a Hilbert space. Further, the analog of "dropping the altitude" of a triangle is the perpendicular projection onto a subspace, which plays a significant role in optimization problems And so on, an element of a Hilbert space can be uniquely specified by its coordinates with respect to a set of coordinate axes (an orthonormal basis), in analogy with Cartesian coordinates in the plane. When that set of