T3Tangent.corewise_inner

t3toolbox.manifold.T3Tangent.corewise_inner(other)

def corewise_inner(self, other: 'T3Tangent'):

The raw corewise (coordinate) dot of two tangents’ variations – not the HS inner product.

Vectorized over the stack: returns an array of shape stack_shape (K + C), one dot per stacked tangent (a scalar when unstacked). The same-frame precondition is checked.

This is the coordinate inner product; it equals Hilbert-Schmidt only on an orthonormal, gauged, (minimal-rank) frame. For that semantic – with the orthogonal/gauge preconditions checked – use ManifoldGeometry.inner() (or CorewiseGeometry.inner() for the Euclidean metric). The gauged identity <v, v'>_HS = sum_i <dU_i, dU_i'> + sum_i <dG_i, dG_i'> is Appendix A.3 of Alger et al. (2026), “Tucker Tensor Train Taylor Series” (arXiv:2603.21141).

Parameters:

other (T3Tangent)