Editing Rank (linear algebra) (section)

==Matrices as tensors==
Matrix rank should not be confused with [[tensor order]], which is called tensor rank. Tensor order is the number of indices required to write a [[tensor]], and thus matrices all have tensor order 2. More precisely, matrices are tensors of type (1,1), having one row index and one column index, also called covariant order 1 and contravariant order 1; see [[Tensor (intrinsic definition)]] for details.

The tensor rank of a matrix can also mean the minimum number of [[simple tensor]]s necessary to express the matrix as a linear combination, and that this definition does agree with matrix rank as here discussed.