Ball (mathematics) - Balls in Normed Vector Spaces

Balls in Normed Vector Spaces

Any normed vector space V with norm |·| is also a metric space, with the metric d(x, y) = |xy|. In such spaces, every ball Br(p) is a copy of the unit ball B1(0), scaled by r and translated by p.

Read more about this topic:  Ball (mathematics)

Famous quotes containing the words balls and/or spaces:

    look the spangles
    that sleep all the year in a dark box
    dreaming of being taken out and allowed to shine,
    the balls the chains red and gold the fluffy threads,

    put up your little arms
    and i’ll give them all to you to hold
    —E.E. (Edward Estlin)

    Surely, we are provided with senses as well fitted to penetrate the spaces of the real, the substantial, the eternal, as these outward are to penetrate the material universe. Veias, Menu, Zoroaster, Socrates, Christ, Shakespeare, Swedenborg,—these are some of our astronomers.
    Henry David Thoreau (1817–1862)