# cirq.linalg.bidiagonalize_unitary_with_special_orthogonals

Finds orthogonal matrices L, R such that L @ matrix @ R is diagonal.

`mat` A unitary matrix.
`rtol` Relative numeric error threshold.
`atol` Absolute numeric error threshold.
`check_preconditions` If set, verifies that the input is a unitary matrix (to the given tolerances). Defaults to set.

A triplet (L, d, R) such that L @ mat @ R = diag(d). Both L and R will be orthogonal matrices with determinant equal to 1.

`ValueError` Matrices don't meet preconditions (e.g. not real).

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