# eigs() Function & Examples

Use the eigs() matrix function in Calcul.io. Review its syntax, edit working examples, understand the result, and explore related math functions.

## eigs

#### eigs(x)

Try it yourself:

```calculio
eigs([[5, 2.3], [2.3, 1]])
eigs([[1, 2, 3], [4, 5, 6], [7, 8, 9]], { precision: 1e-6, eigenvectors: false })
```

[inv](https://calcul.io/function/inv/index.md)

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## eigs(): Eigenvalues and Eigenvectors

**eigs()** finds eigenvalues and associated eigenvectors of a square matrix. An eigenvector keeps its direction under a transformation, changing only by its eigenvalue. These quantities describe stability, principal directions, vibration modes, and repeated transformations.

## Matrix requirements

Eigenvalue problems require a square matrix. Check its dimensions with [size()](https://calcul.io/function/size/index.md). Results can be complex even when all matrix entries are real, so do not discard imaginary parts without a mathematical reason; inspect them with [re()](https://calcul.io/function/re/index.md) and [im()](https://calcul.io/function/im/index.md).

For symmetric matrices, eigenvectors have especially useful orthogonality properties. Related decompositions include [svd()](https://calcul.io/function/svd/index.md) and [qr()](https://calcul.io/function/qr/index.md). Numerical results may vary slightly in ordering or precision, so validate by checking A×v against λ×v using [multiply()](https://calcul.io/function/multiply/index.md).

[All functions](https://calcul.io/functions/index.md)