# Function eigs #

Compute eigenvalues and eigenvectors of a matrix. The eigenvalues are sorted by their absolute value, ascending. An eigenvalue with multiplicity k will be listed k times. The eigenvectors are returned as columns of a matrix – the eigenvector that belongs to the j-th eigenvalue in the list (eg. `values[j]`) is the j-th column (eg. `column(vectors, j)`). If the algorithm fails to converge, it will throw an error – in that case, however, you may still find useful information in `err.values` and `err.vectors`.

## Syntax #

``````math.eigs(x, [prec])
``````

### Parameters #

Parameter Type Description
`x` Array | Matrix Matrix to be diagonalized
`prec` number | BigNumber Precision, default value: 1e-15

### Returns #

Type Description
{values: Array | Matrix, vectors: Array | Matrix} Object containing an array of eigenvalues and a matrix with eigenvectors as columns.

### Throws #

Type | Description —- | ———–

## Examples #

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