R: Matrix Rank

Rank {pracma} | R Documentation

## Matrix Rank

### Description

Provides an estimate of the rank of a matrix `M`.

### Usage

    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))`.

### Note

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

### References

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

### See Also

`nullspace`

### Examples

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

[Package pracma version 2.0.4 Index]