# sf.decompositions.takagi¶

takagi(N, tol=1e-13, rounding=13)[source]

Autonne-Takagi decomposition of a complex symmetric (not Hermitian!) matrix.

Note that singular values of N are considered equal if they are equal after np.round(values, tol).

See [25] and references therein for a derivation.

Parameters
• N (array[complex]) – square, symmetric matrix N

• rounding (int) – the number of decimal places to use when rounding the singular values of N

• tol (float) – the tolerance used when checking if the input matrix is symmetric: $$|N-N^T| <$$ tol

Returns

(rl, U), where rl are the (rounded) singular values,

and U is the Takagi unitary, such that $$N = U \diag(rl) U^T$$.

Return type

tuple[array, array]