# Find Eigenvalues and Eigenvectors of a Matrix in R Programming – eigen() Function

`eigen()` function in R Language is used to calculate eigenvalues and eigenvectors of a matrix. Eigenvalue is the factor by which a eigenvector is scaled.

Syntax: eigen(x)

Parameters:
x: Matrix

Example 1:

 `# R program to illustrate  ` `# Eigenvalues and eigenvectors of matrix  ` `   `  `# Create a 3x3 matrix  ` `A ``=` `matrix(c(``1``:``9``), ``3``, ``3``)  ` ` `  `cat(``"The 3x3 matrix:\n"``)  ` `print``(A)  ` `   `  `# Calculating Eigenvalues and eigenvectors  ` `print``(eigen(A))  `

Output:

```The 3x3 matrix:
[, 1] [, 2] [, 3]
[1, ]    1    4    7
[2, ]    2    5    8
[3, ]    3    6    9
eigen() decomposition
\$values
  1.611684e+01 -1.116844e+00 -5.700691e-16

\$vectors
[, 1]       [, 2]       [, 3]
[1, ] -0.4645473 -0.8829060  0.4082483
[2, ] -0.5707955 -0.2395204 -0.8164966
[3, ] -0.6770438  0.4038651  0.4082483
```

Example 2:

 `# R program to illustrate  ` `# Eigenvalues and eigenvectors of matrix  ` `   `  `# Create a 3x3 matrix  ` `A ``=` `matrix(c(``2``, ``3``, ``5``, ``1``), ``2``, ``2``)  ` `A  ` `   `  `# Calculating Eigenvalues and eigenvectors  ` `print``(eigen(A))  `

Output:

```     [, 1] [, 2]
[1, ]    2    5
[2, ]    3    1
eigen() decomposition
\$values
  5.405125 -2.405125

\$vectors
[, 1]       [, 2]
[1, ] 0.8265324 -0.7503320
[2, ] 0.5628892  0.6610612
```
My Personal Notes arrow_drop_up Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Article Tags :

Be the First to upvote.

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.