# tf.svd(tensor, full_matrices=False, compute_uv=True, name=None)

### tf.svd(tensor, full_matrices=False, compute_uv=True, name=None)

See the guide: Math > Matrix Math Functions

Computes the singular value decompositions of one or more matrices.

Computes the SVD of each inner matrix in tensor such that tensor[..., :, :] = u[..., :, :] * diag(s[..., :, :]) * transpose(v[..., :, :])

# a is a tensor.
# s is a tensor of singular values.
# u is a tensor of left singular vectors.
#v is a tensor of right singular vectors.
s, u, v = svd(a)
s = svd(a, compute_uv=False)


#### Args:

• tensor: Tensor of shape [..., M, N]. Let P be the minimum of M and N.
• full_matrices: If true, compute full-sized u and v. If false (the default), compute only the leading P singular vectors. Ignored if compute_uv is False.
• compute_uv: If True then left and right singular vectors will be computed and returned in u and v, respectively. Otherwise, only the singular values will be computed, which can be significantly faster.
• name: string, optional name of the operation.

#### Returns:

• s: Singular values. Shape is [..., P].
• u: Right singular vectors. If full_matrices is False (default) then shape is [..., M, P]; if full_matrices is True then shape is [..., M, M]. Not returned if compute_uv is False.
• v: Left singular vectors. If full_matrices is False (default) then shape is [..., N, P]. If full_matrices is True then shape is [..., N, N]. Not returned if compute_uv is False.

#### numpy compatibility

Mostly equivalent to numpy.linalg.svd, except that the order of output arguments here is s, u, v when compute_uv is True, as opposed to u, s, v for numpy.linalg.svd.