Rank Nullity Theorem
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 kerne...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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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