# 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 ```js 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 ```js 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 ``` ## See also [inv](inv.md)