Statistics Dictionary

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Matrix Rank

You can think of an r x c matrix as a set of r row vectors, each having c elements; or you can think of it as a set of c column vectors, each having r elements.

The rank of a matrix is a measure of the linear dependence of its vectors. For an r x c matrix,

  • If r is less than c, then the rank of the matrix is the maximum number linearly independent row vectors in the matrix.

  • If r is greater than c, then the rank of the matrix is the maximum number linearly independent column vectors in the matrix.

  • If r is equal to c, then the rank of the matrix is the maximum number of linearly independent row vectors or the maximum number of linearly independent column vectors. (When r equals c, the maximum number of linearly independent row vectors equals the maximum number of linearly independent column vectors.)

See also:  Matrix Rank | Echelon Matrices