, while the row rank of is the dimension of the row space of .

A fundamental result in linear algebra is that the column rank and the row rank are always equal. (Three proofs of this result are given in , below.) This number (i.e., the number of linearly independent rows or columns) is simply called the rank of .

A matrix is said to have full rank if its rank equals the largest possible for a matrix of the same dimensions, which is the lesser of the number of rows and columns.

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