# How to obtain eigenvalues

## What is an eigenvalue?

Eigenvalues (also called characteristic values or latent roots) are the variances of the principal components. Minitab calculates eigenvalues when you perform a principal components analysis.

###### Note

For Factor Analysis, Minitab only calculates eigenvalues when you choose principal components as the method of extraction.

## Obtain eigenvalues for principal components by using only a correlation matrix or a covariance matrix

To obtain eigenvalues using only a correlation matrix or covariance matrix, use Factor Analysis instead of Principal Components Analysis. Suppose the covariance matrix is in columns C1-C3:

1. Choose Data > Copy > Columns to Matrix.
2. In Copy from columns, enter C1-C3.
3. For In current worksheet, in matrix:, enter M1. Click OK.
4. Choose Stat > Multivariate > Factor Analysis.
5. Click Options.
6. For Matrix to Factor, choose Covariance.
7. For Source of Matrix, choose Use matrix and enter M1.
8. Click OK in each dialog box.

In the output, the eigenvalues are under Variance (in Factor Analysis, the eigenvalues are the variances of the principal components).

## Obtain eigenvalues for a matrix that was factored in factor analysis

You can use either Factor Analysis or Eigen Analysis to obtain the eigenvalues.

• Store the eigenvalues using Factor Analysis.
1. Choose Stat > Multivariate > Factor Analysis.
2. Click Storage.
3. In the field beside Eigenvalues, enter a column in which to store the eigenvalues. Underneath, enter a matrix in which to store the eigenvectors of the matrix that was factored.
Minitab stores eigenvalues in numerical order from largest to smallest.
• Store the eigenvalues using Eigen Analysis.

Suppose your variables are in columns C1-C5, and you want to store the eigenvalues in column C6:

1. Choose Stat > Basic Statistics > Correlation.
2. In Variables, enter C1-C5.
3. Select Store matrix (display nothing). Click OK.
4. Choose Calc > Matrices > Eigen Analysis.
5. In Analyze matrix, enter CORR1.
6. In Column of eigenvalues, enter C6. Click OK.
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