linalg op• Data kinds: matrix → table
• Call: import fullseye as fs; fs.ledger.mat_eig(a) (to call the implementation directly, import mathops; mathops.mat_eig(a); from the registry, opsmath.get("mat_eig"))
Eigen-decomposition of a general square matrix A V = V diag(w) (complex in general).
The non-symmetric companion of mat_eigh: a rotation has eigenvalues e^{±iθ}, a Markov matrix has eigenvalue 1 with the stationary distribution as eigenvector. Also returns the eigenvector condition number cond_V = κ(V): near-defective matrices (a Jordan block nudged by 1e-10) have κ(V) ~ 1e5+ and their eigenvalues move by √ of a perturbation — computed, not hidden.
Returns a dict: w (complex, sorted by descending |w|), V (columns, unit 2-norm), residual = max|AV − V diag(w)| / max|A|, cond_V.
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.
• (none yet)
table as input)dynsys_poincare_section · dwt_inverse · chebyshev_eval_nd
linalg)mat_solve · mat_lstsq · mat_svd · mat_eigh · mat_pinv · mat_cond · mat_lu · mat_qr
*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.