# How to find power of a matrix in R?

The power of a matrix in R cannot be found directly because there is not function in base R for that. Therefore, for this purpose we can use %^% of expm package. Firstly, we will install the expm package then load it and use %^%. For example, suppose we have a matrix called M and we want to find the M raise to the power 2 then it can be done as − M %^%2

## Example

install.packages("expm")
library(expm)

## Example

Live Demo

M1<-matrix(1:25,nrow=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

PowerM1<-M1%^%2
PowerM1

## Output

    [,1] [,2] [,3] [,4] [,5]
[1,] 215  490  765 1040 1315
[2,] 230  530  830 1130 1430
[3,] 245  570  895 1220 1545
[4,] 260  610  960 1310 1660
[5,] 275  650 1025 1400 1775

## Example

Live Demo

M2<-matrix(sample(1:10,36,replace=TRUE),nrow=6)
M2

## Output

   [,1] [,2] [,3] [,4] [,5] [,6]
[1,] 3    1    5    4    6    8
[2,] 7    1    9    2    3    1
[3,] 6    8    4    9    3    6
[4,] 6    3    7    6    9    10
[5,] 7    1    5    5    6    8
[6,] 3    9    4    10   3    10

## Example

PowerM2<-M2%^%5
PowerM2

## Output

      [,1]    [,2]    [,3]    [,4]    [,5]    [,6]
[1,] 5677617 4739628 6065058 7081674 5548641 8398595
[2,] 4479295 3740518 4785348 5588349 4377963 6627882
[3,] 7079665 5917035 7556600 8838028 6916227 10476843
[4,] 8396194 7011395 8967480 10474806 8204430 12421001
[5,] 6592060 5505091 7039821 8224081 6440718 9751106
[6,] 7884913 6587253 8417738 9840903 7704426 11668026

## Example

Live Demo

M3<-matrix(sample(1:50,36),ncol=6)
M3

## Output

   [,1] [,2] [,3] [,4] [,5] [,6]
[1,] 10  4    45   19   17    38
[2,] 29  46   28   27   41    40
[3,] 33  13   34   25   32    44
[4,] 2   16   7    39   23    26
[5,] 18  3    6    36   20    21
[6,] 8   12   47   24   48    49

## Example

PowerM3<-M3%^%2
PowerM3

## Output

     [,1] [,2] [,3] [,4] [,5] [,6]
[1,] 2349 1620 4113 3688 4375 5233
[2,] 3660 3631 5860 5982 6636 7697
[3,] 2807 2196 5440 5011 5509 6748
[4,] 1415 1840 2409 3618 3519 3795
[5,] 1065 1176 2457 3201 2857 3453
[6,] 3283 2311 5053 5491 5996 6885

## Example

Live Demo

M4<-matrix(sample(1:50,100,replace=TRUE),ncol=10)
M4

## Output

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

## Example

PowerM4<-M4%^%2
PowerM4

## Output

    [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,] 3832 8661 6240 3615 7610 7854 6660 6923 6274 3534
[2,] 5183 9568 5469 4276 7979 7891 6337 6571 5815 3653
[3,] 5359 8378 7006 5385 8373 10475 9294 7219 6551 6790
[4,] 3603 6376 6628 4453 6581 8304 7126 6141 4600 5153
[5,] 6483 10241 7044 5898 9008 10430 8618 7793 7034 5717
[6,] 6432 7345 6783 6596 7825 11111 7150 9289 6433 5777
[7,] 4531 6863 5664 4518 6320 8695 6486 6978 4378 5971
[8,] 4769 5906 5711 4483 5927 8056 6149 6824 4836 5144
[9,] 4641 5794 7022 3365 6615 7067 5294 6310 4342 4091
[10,] 3754 5193 5687 3389 5471 6937 5509 6230 4128 4321

## Example

Live Demo

M5<-matrix(rnorm(36,2,5),ncol=6)
M5

## Output

      [,1]       [,2]       [,3]    [,4]       [,5]    [,6]
[1,] 6.3775900 1.3315642 16.556120 6.7855167 1.448674 -0.4512223
[2,] -1.4833206 1.4107878 10.934331 5.3026678 4.185240 1.3263026
[3,] 5.2464593 0.7680077 5.282309 5.8267211 2.290441 -3.2177754
[4,] 1.1926252 6.2123900 -3.914076 -0.8400293 6.985479 1.0936410
[5,] -3.0834922 5.2982841 -2.171566 12.1644126 9.244374 2.4343071
[6,] -0.8845731 1.6943283 5.397350 -5.6692890 5.394338 -9.0250482

## Example

PowerM5<-M5%^%2
PowerM5

## Output

      [,1]       [,2]    [,3]       [,4]       [,5]    [,6]
[1,] 129.58427 72.15120 175.462119 161.28433 111.09090 -39.36579
[2,] 38.05959  65.77686 25.941451  100.06454 111.68620 -28.62635
[3,] 62.76688  55.00765 78.013912  111.66072 67.43189   22.64256
[4,] -45.65285 40.99183 61.019494  97.70832  83.37095   26.51194
[5,] -55.06803 130.37502 -59.136745 82.95197 196.29795  29.24349
[6,] 4.75088   -16.57282 -5.843755  155.97795 -20.24755  73.66168

## Example 6

Live Demo

M6<-matrix(rpois(36,5),ncol=6)
M6

## Output

   [,1] [,2] [,3] [,4] [,5] [,6]
[1,] 4    7    11   8    3    4
[2,] 4    5    7    6    5    6
[3,] 6    1    2    7    4    1
[4,] 5    8    4    6    7    3
[5,] 7    2    3    5    7    2
[6,] 9    7    3    7    1    2

Example

PowerM6<-M6%^%3
PowerM6

## Output

    [,1] [,2] [,3] [,4] [,5] [,6]
[1,] 5901 5506 5622 6925 5158 3312
[2,] 5271 4988 5166 6261 4618 3022
[3,] 3663 3259 3376 4264 3201 2043
[4,] 5599 5021 5139 6482 4769 3047
[5,] 4395 3950 4091 5141 3819 2422
[6,] 5282 4638 4659 6103 4459 2865

Updated on: 08-Sep-2020

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