# cirq.bidiagonalize_real_matrix_pair_with_symmetric_products

Finds orthogonal matrices that diagonalize both mat1 and mat2.

Requires mat1 and mat2 to be real. Requires mat1.T @ mat2 to be symmetric. Requires mat1 @ mat2.T to be symmetric.

`mat1` One of the real matrices.
`mat2` The other real matrix.
`rtol` Relative numeric error threshold.
`atol` Absolute numeric error threshold.
`check_preconditions` If set, verifies that the inputs are real, and that mat1.T @ mat2 and mat1 @ mat2.T are both symmetric. Defaults to set.

A tuple (L, R) of two orthogonal matrices, such that both L @ mat1 @ R and L @ mat2 @ R are diagonal matrices.

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

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{"lastModified": "Last updated 2024-06-27 UTC."}