NIKX-Tech/numx

linalg: QR decomposition (Householder)

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#82 建立於 2026年7月11日

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Add numx_qr_decompose to the linalg module: QR decomposition via Householder reflections, bounded by NUMX_MAX_MAT_ROWS/NUMX_MAX_MAT_COLS like the rest of linalg (see numx_lu_decompose and numx_cholesky_decompose, #51, for the established style of matrix decomposition functions in this codebase).

Follow CONTRIBUTING.md exactly: full Doxygen header, NULL-checks, numx_status_t return, all four deliverables (header, impl, test, docs page). Test against known QR examples and verify Q is orthogonal (Q^T Q = I) and QR reconstructs the original matrix, following the same reconstruction-test pattern #51 used for Cholesky (test_cholesky_decompose_residual_reconstruction in tests/test_linalg.c).

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