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# 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]  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
[1]  5.405125 -2.405125

\$vectors
[, 1]       [, 2]
[1, ] 0.8265324 -0.7503320
[2, ] 0.5628892  0.6610612
```
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