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Rank of a Matrix

Source: R/R.R
R.Rd

Returns the rank of a matrix X, using the QR decomposition, QR. Included here as a simple function, because rank does something different and it is not obvious what to use for matrix rank.

Usage

R(X)

Arguments

X

a matrix

Value

rank of X

See also

qr

Examples

M <- outer(1:3, 3:1)
M
#>      [,1] [,2] [,3]
#> [1,]    3    2    1
#> [2,]    6    4    2
#> [3,]    9    6    3
R(M)
#> [1] 1

M <- matrix(1:9, 3, 3)
M
#>      [,1] [,2] [,3]
#> [1,]    1    4    7
#> [2,]    2    5    8
#> [3,]    3    6    9
R(M)
#> [1] 2
# why rank=2?
echelon(M)
#>      [,1] [,2] [,3]
#> [1,]    1    0   -1
#> [2,]    0    1    2
#> [3,]    0    0    0

set.seed(1234)
M <- matrix(sample(1:9), 3, 3)
M
#>      [,1] [,2] [,3]
#> [1,]    6    1    7
#> [2,]    5    8    9
#> [3,]    4    2    3
R(M)
#> [1] 3