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How to check if a matrix is invertible or not in R?
If the matrix is singular then it is not invertible and if it is non−singular then it is invertible. Therefore, we can check if a matrix is singular or not. We can use is.singular.matrix function of matrixcalc for this purpose. For example, if we have a matrix called M then to check whether it is invertible or not, we can use is.singular.matrix(M).
Example1
Loading matrixcalc package and creating a matrix −
library(matrixcalc) M1<−matrix(1:25,ncol=5) M1
Output
[,1] [,2] [,3] [,4] [,5] [1,] 1 6 11 16 21 [2,] 2 7 12 17 22 [3,] 3 8 13 18 23 [4,] 4 9 14 19 24 [5,] 5 10 15 20 25
Example
is.singular.matrix(M1)
Output
[1] TRUE
It means M1 is not invertible.
Example2
M2<−matrix(rpois(64,8),nrow=8) M2
Output
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [1,] 4 3 9 9 7 8 6 1 [2,] 5 8 8 10 12 9 8 6 [3,] 6 6 7 14 9 11 13 8 [4,] 6 7 10 4 6 8 8 7 [5,] 13 8 10 6 3 7 9 4 [6,] 7 10 14 8 8 5 7 2 [7,] 3 9 7 9 6 4 6 8 [8,] 5 9 13 6 8 15 8 2
Example
is.singular.matrix(M2)
Output
[1] FALSE
It means M2 is invertible.
Example3
M3<−matrix(rpois(36,5),nrow=6) M3
Output
[,1] [,2] [,3] [,4] [,5] [,6] [1,] 1 8 5 5 8 4 [2,] 4 9 4 2 4 6 [3,] 2 5 1 7 7 4 [4,] 4 4 1 7 5 2 [5,] 6 6 2 4 6 10 [6,] 9 6 1 4 9 3
Example
is.singular.matrix(M3)
Output
[1] FALSE
It means M3 is invertible.
Example4
M4<−matrix(rnorm(36),nrow=6) M4
Output
[,1] [,2] [,3] [,4] [,5] [,6] [1,] −0.2336251 0.3096045 −0.8818330 −0.04347818 −0.1778513 −0.4080015 [2,] −1.2177266 2.1817922 −0.9377145 −1.78284702 0.4995368 −1.3991093 [3,] 1.2766525 −0.2323218 0.8519997 0.31299613 −0.6803835 −1.1479453 [4,] 0.7903845 0.9700842 0.5117611 1.19601996 0.5250466 1.6161917 [5,] −1.3520358 0.6123879 1.9760799 −2.26366053 −1.4070510 0.8421128 [6,] 0.7777491 −2.0503730 −0.2613909 −1.35740539 0.9093589 0.9895680
Example
is.singular.matrix(M4)
Output
[1] FALSE
It means M4 is invertible.
Example5
M5<−matrix(runif(25,2,5),nrow=5) M5
Output
[,1] [,2] [,3] [,4] [,5] [1,] 4.576693 3.199907 4.005826 2.526450 3.443598 [2,] 2.470785 2.327514 2.169090 4.098793 3.940592 [3,] 4.547359 4.909557 3.066596 2.676077 3.837429 [4,] 4.135820 2.309655 3.839309 3.164276 3.802660 [5,] 2.634209 3.422963 3.619294 2.017092 3.601271
Example
is.singular.matrix(M5)
Output
[1] FALSE
It means M5 is invertible.
Example6
M6<−matrix(rexp(25,1.25),nrow=5) M6
Output
[,1 ] [,2] [,3] [,4] [,5] [1,] 0.1643510 0.1040981 0.584215338 2.2388616 0.05568353 [2,] 0.1125260 0.6645813 0.004011225 0.4228827 2.27699989 [3,] 0.7495866 1.3936340 0.823750284 0.9881828 0.51836239 [4,] 0.2237822 2.6784765 0.614246592 1.1034886 1.11131293 [5,] 3.9557367 1.4623781 0.594690357 0.4180981 0.70791124
Example
is.singular.matrix(M6)
Output
[1] FALSE
It means M6 is invertible.
Example7
M7<−matrix(rpois(64,2),ncol=8) M7
Output
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [1,] 2 2 1 1 2 2 2 1 [2,] 3 3 1 2 4 0 1 1 [3,] 0 3 1 3 2 2 1 2 [4,] 2 1 2 1 2 1 1 4 [5,] 2 3 0 2 0 2 1 1 [6,] 3 2 6 1 0 1 2 2 [7,] 4 1 3 4 2 2 3 4 [8,] 2 0 1 2 4 2 1 1
Example
is.singular.matrix(M7)
Output
[1] FALSE
It means M7 is invertible.
Example8
M8<−matrix(rnorm(16,5,2.1),ncol=4) M8
Output
[,1] [,2] [,3] [,4] [1,] 4.058489 6.951464 4.846994 6.376624 [2,] 3.786127 10.430663 6.350964 4.439200 [3,] 4.166099 1.210901 7.712636 5.234337 [4,] 2.068379 4.461313 4.033786 3.732698
Example
is.singular.matrix(M8)
Output
[1] FALSE
It means M7 is invertible.
Updated on: 05-Feb-2021
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