linalg op• Data kinds: matrix → measurement
• Call: import fullseye as fs; fs.ledger.mat_cond(a) (to call the implementation directly, import mathops; mathops.mat_cond(a); from the registry, opsmath.get("mat_cond"))
Spectral (2-norm) condition number s_max / s_min — the numerical canary of the whole linalg family.
cond == 1 for an orthogonal/orthonormal matrix (the best possible); inf (returned, not raised — the question "how conditioned is it?" has that honest answer) for an exactly singular one. A solve against *A* loses roughly log10(cond(A)) significant digits (Golub & Van Loan §2.6):
• cond ~ 1e3 — comfortable, ~13 digits survive.
• cond ~ 1e8 — half the digits are gone; residuals may still look small while parameters are off.
• cond > 1e12 — do not trust mat_solve here: at best ~3 digits remain. Rescale/centre the problem, or switch to mat_lstsq / mat_pinv with an honest rcond.
Defined for any rectangular (m, n) matrix (via its singular values).
HALCON: no direct operator (combine norm_matrix of *A* and of its inverse).
Every mathops op validates its input before computing (nothing slips through silently):
• complex input raises ValueError — coercing to float64 silently discards the imaginary part (numpy only emits a ComplexWarning and returns a plausible-looking wrong real number). State .real/.imag/abs() explicitly, or use complexops, which handles complex data.
• masked arrays with masked elements raise ValueError — the implicit conversion that peels off the mask and uses the raw values underneath is refused. Say explicitly whether to fill or to drop.
• NaN/Inf raises ValueError on every input (refused with the count stated — it propagates through the whole result).
• Shapes are strict: 1-D and 2-D are never implicitly promoted or broadcast (a matrix in a vector slot, or a vector in a matrix slot, raises ValueError; reshape explicitly).
• Size cap: ops that take a matrix, and the stat_histogram bins, raise ValueError beyond mathops.MAX_ELEMENTS (2^26 ≈ 67 million elements).
• blas_threads_and_memory — Why matrix decompositions are slow — BLAS threads, caches, memory layout
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• math_metrology — py -3.11 examples/math_metrology.py
measurement as input)—
linalg)mat_solve · mat_lstsq · mat_svd · mat_eigh · mat_pinv · mat_lu · mat_qr · mat_cholesky
*Provenance: mathops.py — MATH operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.