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)
“The peculiarity of sculpture is that it creates a three-dimensional object in space. Painting may strive to give on a two-dimensional plane, the illusion of space, but it is space itself as a perceived quantity that becomes the peculiar concern of the sculptor. We may say that for the painter space is a luxury; for the sculptor it is a necessity.”
—Sir Herbert Read (1893–1968)