mathjs/docs/reference/functions/eigs.md

Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser with support for symbolic computation, comes with a large set of built-in functions and constants, and offers an integrated solution to work with dif

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# Function eigs

Compute eigenvalue and eigenvector of a real symmetric matrix.
Only applicable to two dimensional symmetric matrices. Uses Jacobi
Algorithm. Matrix containing mixed type ('number', 'bignumber', 'fraction')
of elements are not supported. Input matrix or 2D array should contain all elements
of either 'number', 'bignumber' or 'fraction' type. For 'number' and 'fraction', the
eigenvalues are of 'number' type. For 'bignumber' the eigenvalues are of ''bignumber' type.
Eigenvectors are always of 'number' type.


## Syntax

```js
math.eigs(x)
```

### Parameters

Parameter | Type | Description
--------- | ---- | -----------
`x` | Array &#124; Matrix | Matrix to be diagonalized

### Returns

Type | Description
---- | -----------
{values: Array, vectors: Array} &#124; {values: Matrix, vectors: Matrix} | Object containing eigenvalues (Array or Matrix) and eigenvectors (2D Array/Matrix with eigenvectors as columns).


## Examples

```js
const H = [[5, 2.3], [2.3, 1]]
const ans = math.eigs(H) // returns {values: [E1,E2...sorted], vectors: [v1,v2.... corresponding vectors as columns]}
const E = ans.values
const U = ans.vectors
math.multiply(H, math.column(U, 0)) // returns math.multiply(E[0], math.column(U, 0))
const UTxHxU = math.multiply(math.transpose(U), H, U) // rotates H to the eigen-representation
E[0] == UTxHxU[0][0]  // returns true
```


## See also

[inv](inv.md)