High Quality Content by WIKIPEDIA articles! In mathematics, the rank–nullity theorem of linear algebra, in its simplest form, states that the rank and the nullity of a matrix add up to the number of columns of the matrix. Specifically, if A is an m-by-n matrix over the field F, then rank A + nullity A = n.This applies to linear maps as well. Let V and W be vector spaces over the field F and let T : V ? W be a linear map. Then the rank of T is the dimension of the image of T, the nullity the dimension of the kernel of T, and we have dim (im T) + dim (ker T) = dim V or, equivalently, rank T + nullity T = dim V.

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