In linear algebra, the column space, C(A) of a matrix (sometimes called the range of a matrix) is the set of all possible linear combinations of its column vectors. The column space of an m × n matrix is a subspace of m-dimensional Euclidean space. The dimension of the column space is called the rank of the matrix.
The column space of a matrix is the image or range of the corresponding matrix transformation.
Read more about Column Space: Definition, Basis, Dimension, Relation To The Left Null Space
Famous quotes containing the words column and/or space:
“I stand on top
of our back steps and breathe the rich air—
a mother skunk with her column of kittens swills the garbage pail.
She jabs her wedge-head in a cup
of sour cream, drops her ostrich tail,
and will not scare.”
—Robert Lowell (1917–1977)
“In bourgeois society, the French and the industrial revolution transformed the authorization of political space. The political revolution put an end to the formalized hierarchy of the ancien regimé.... Concurrently, the industrial revolution subverted the social hierarchy upon which the old political space was based. It transformed the experience of society from one of vertical hierarchy to one of horizontal class stratification.”
—Donald M. Lowe, U.S. historian, educator. History of Bourgeois Perception, ch. 4, University of Chicago Press (1982)