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 tensors necessary to express the matrix as a linear combination, and that this definition does agree with matrix rank as here discussed. See also Matroid rank Nonnegative rank (linear algebra) Rank (differential topology) Multicollinearity Linear dependence Notes References Sources Further reading Kaw, Autar K. Two Chapters from the book Introduction to Matrix Algebra: 1. Vectors and System of Equations Mike Brookes: Matrix Reference Manual. Linear algebra