Matrix Rank

Provides an estimate of the rank of a matrix M.

Rank(M)

Arguments

M

Numeric matrix; vectors will be considered as column vectors.

Details

Provides an estimate of the number of linearly independent rows or columns of a matrix M. Compares an approach using QR-decomposition with one counting singular values larger than a certain tolerance (Matlab).

Value

Matrix rank as integer between 0 and min(ncol(M), nrow(M)).

References

Trefethen, L. N., and D. Bau III. (1997). Numerical Linear Algebra. SIAM, Philadelphia.

Note

The corresponding function in Matlab is called rank, but that term has a different meaning in R.

See also

nullspace

Examples

Rank(magic(10))   #=> 7
#> [1] 7
Rank(magic(100))  #=> 3 (!)
#> [1] 3
Rank(hilb(8))     #=> 8 , but qr(hilb(8))$rank says, rank is 7.
#> Warning: Rank calculation may be problematic.
#> [1] 8
# Warning message:
# In Rank(hilb(8)) : Rank calculation may be problematic.