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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