Linear Independence - Projective Space of Linear Dependences

Projective Space of Linear Dependences

A linear dependence among vectors v1, ..., vn is a tuple (a1, ..., an) with n scalar components, not all zero, such that

If such a linear dependence exists, then the n vectors are linearly dependent. It makes sense to identify two linear dependences if one arises as a non-zero multiple of the other, because in this case the two describe the same linear relationship among the vectors. Under this identification, the set of all linear dependences among v1, ...., vn is a projective space.

Read more about this topic:  Linear Independence

Famous quotes containing the word space:

    To play is nothing but the imitative substitution of a pleasurable, superfluous and voluntary action for a serious, necessary, imperative and difficult one. At the cradle of play as well as of artistic activity there stood leisure, tedium entailed by increased spiritual mobility, a horror vacui, the need of letting forms no longer imprisoned move freely, of filling empty time with sequences of notes, empty space with sequences of form.
    Max J. Friedländer (1867–1958)