In mathematics, specifically linear algebra and geometry, relative dimension is the dual notion to codimension.
In linear algebra, given a quotient map, the difference dim V − dim Q is the relative dimension; this equals the dimension of the kernel.
In fiber bundles, the relative dimension of the map is the dimension of the fiber.
More abstractly, the codimension of a map is the dimension of the cokernel, while the relative dimension of a map is the dimension of the kernel.
These are dual in that the inclusion of a subspace of codimension k dualizes to yield a quotient map of relative dimension k, and conversely.
The additivity of codimension under intersection corresponds to the additivity of relative dimension in a fiber product.
Just as codimension is mostly used for injective maps, relative dimension is mostly used for surjective maps.
Famous quotes containing the words relative and/or dimension:
“It is an interesting question how far men would retain their relative rank if they were divested of their clothes.”
—Henry David Thoreau (1817–1862)
“God cannot be seen: he is too bright for sight; nor grasped: he is too pure for touch; nor measured: for he is beyond all sense, infinite, measureless, his dimension known to himself alone.”
—Marcus Minucius Felix (2nd or 3rd cen. A.D.)