[j45856021-dev]

Fixes #99.

Use a positive diagonal (1 + torch.rand(...)) consistently in all three low-rank solve examples, following the maintainer guidance in the issue. The manual Woodbury comparison also needs an identity sized by the rank of C, not its row count, and a column-shaped RHS for torch.cholesky_solve; the result is squeezed back to the documented vector shape.

This changes only README.md, which is also the source for the corresponding Sphinx index section. No operator implementation changes.

Validation

• Executed the README examples with their sample assignments uncommented, using CPU float32/float64 and seeds 0 and 13. All 14 local example/control cases pass, including the full 1,000-row examples and comparisons against dense torch.linalg.solve. The original README produced 12 failing cases: non-positive-definite matrices, a rank/row size mismatch, and a one-dimensional Cholesky-solve RHS.
• All 183 existing tests in test.operators.test_low_rank_root_added_diag_linear_operator pass. Environment: Python 3.13.16, PyTorch 2.14.1, macOS arm64.
• The Sphinx HTML build with -W --keep-going succeeds, and the three changed code blocks match the rendered HTML. Both baseline and patched builds emit the same 55 existing Python RuntimeWarnings from the type-hint formatter in conf.py; neither build is warning-free.
• git diff --check and the applicable README text checks pass.

The 10-million-row example was exercised at 64 rows, not allocated in full. The full repository suite, minimum-version/GPU matrix and pre-commit orchestration were not run; applicable text checks were checked independently.

AI disclosure: Prepared and checked autonomously with GPT-6 Astra. No human review is claimed.