How to find the rank of a matrix in R?

The rank of a matrix is defined as the maximum number of linearly independent vectors in rows or columns. If we have a matrix with dimensions R x C, having R number of rows and C number of columns, and if R is less than C then the rank of the matrix would be R. To find the rank of a matrix in R, we can use rankMatrix function in Matrix package.

Loading Matrix package −

library(Matrix)

Example

 Live Demo

M1<-matrix(1:9,ncol=3) M1

Output

[,1] [,2] [,3] [1,] 1 4 7 [2,] 2 5 8 [3,] 3 6 9

rankMatrix(M1) [1] [1] 2

Example

 Live Demo

M2<-matrix(1:36,nrow=6) M2

Output

    [,1] [,2] [,3] [,4] [,5] [,6] [1,]  1    7   13 19 25 31 [2,]  2    8   14 20 26 32 [3,]  3    9   15 21 27 33 [4,]  4    10 16 22 28 34 [5,]  5    11  18 24 30 36

rankMatrix(M2) [1] [1] 2

Example

 Live Demo

M3<-matrix(sample(0:9,100,replace=TRUE),nrow=20) M3

Output

[,1] [,2] [,3] [,4] [,5] [1,] 9 8 1 4 1 [2,] 5 3 0 6 1 [3,] 2 6 5 5 4 [4,] 5 8 3 7 5 [5,] 3 1 4 0 3 [6,] 1 5 5 3 5 [7,] 0 3 0 3 5 [8,] 1 9 4 0 4 [9,] 1 4 3 7 6 [10,] 1 3 6 1 4 [11,] 6 9 2 5 9 [12,] 7 0 2 8 1 [13,] 5 9 4 1 1 [14,] 9 1 1 6 4 [15,] 1 4 4 0 7 [16,] 6 0 9 2 7 [17,] 9 3 0 2 1 [18,] 9 6 0 7 2 [19,] 5 2 0 8 5 [20,] 8 8 4 0 4

rankMatrix(M3) [1] [1] 5

Example

 Live Demo

M4<-matrix(sample(21:50,160,replace=TRUE),nrow=20) M4

Output

    [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [1,] 49   35   25 36 31 22 49 42 [2,] 45   33   21 39 37 26 41 37 [3,] 36   30   46 50 26 32 24 49 [4,] 33   39   31 39 37 50 50 32 [5,] 41   38   39 38 40 25 42 30 [6,] 34   49   26 34 24 34 42 26 [7,] 40   44   30 21 27 47 32 47 [8,] 35   27   21 25 37 28 48 27 [9,] 34   50   41 38 39 27 43 40 [10,] 21 41 50 28 32 38 22 25 [11,] 26  46 34 29 24 38 28 39 [12,] 36  41 36 47 49 48 49 31 [13,] 44  50 37 38 33 26 37 45 [14,] 31  22 47 37 47 41 23 45 [15,] 42  39 38 26 35 21 31 31 [16,] 50  29 40 47 48 34 23 29 [17,] 49  21 30 47 24 21 43 47 [18,] 27  22 25 34 45 28 49 45 [19,] 38  39 32 31 29 23 34 45 [20,] 45  37 31 43 40 27 29 36

rankMatrix(M4) [1] [1] 8

Example

 Live Demo

M5<-matrix(sample(rnorm(20),25,replace=TRUE),nrow=5) M5

Output

[,1] [,2] [,3] [,4] [,5] [1,] 0.73475325 -1.2186186 -0.21496111 1.8642877 1.1133489 [2,] -0.09091262 -0.4513579 0.18346741 0.1834674 -0.4513579 [3,] 1.55003168 -0.1454168 0.28244025 0.5674004 1.5706586 [4,] -0.90693971 -1.2186186 -0.09091262 -0.1454168 1.0289755 [5,] -0.45135792 0.5674004 0.28244025 -0.2149611 1.5500317

rankMatrix(M5) [1] [1] 5

Example

 Live Demo

M6<-matrix(sample(rexp(5,2),20,replace=TRUE),nrow=10) M6

Output

[,1] [,2] [1,] 0.2969787 3.5003481 [2,] 0.5462926 3.5003481 [3,] 1.0018821 0.5462926 [4,] 3.5003481 0.2969787 [5,] 1.0018821 0.2969787 [6,] 1.0018821 0.2969787 [7,] 1.0018821 0.5462926 [8,] 0.2133455 0.2133455 [9,] 0.5462926 3.5003481 [10,] 0.2969787 0.2133455

rankMatrix(M6) [1] [1] 2