What question did this study set out to answer?

The study aims to reframe standard linear algebra matrices as Clifford multivector networks and develop phase-rotor methods for matrix decomposition and joint diagonalization without standard LAPACK/BLAS dependencies.

August 15, 2026Open Access

Phase Algebra: Matrices as Clifford Multivector Networks & Phase-Rotor Methods for SVD and Joint Diagonalization (An Extension of Linear Algebra) | (A Rust Prototype) | wAI ~ wErrors

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AKArtiom KovnatskyWeatherford College

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Implication

Computational study demonstrates phase-rotor methods for matrix decomposition in numerical linear algebra, suggesting an alternative ontology for photonic hardware execution.

Key Points

The study aims to reframe standard linear algebra matrices as Clifford multivector networks and develop phase-rotor methods for matrix decomposition and joint diagonalization without standard LAPACK/BLAS dependencies.
Modeled matrix rows and columns as coupled generator families using Clifford multivector fields (Cl_{2,0} and Cl_{4,0}).
Formulated SVD as phase alignment on U(1) x U(1) phase lines with conserved local moduli, utilizing irrational golden-ratio phase dispersion to resolve degenerate spectra.
Implemented algorithms in a standalone Rust library without LAPACK or BLAS dependencies and designed a photonic compiler generating Mach–Zehnder Interferometer execution schedules.
Layer-0 golden pre-spin phase dispersion locked degenerate spectra down to 10^-11 precision.
Unified phase engine successfully solved Square SVD, Complex U(N) SVD, Phase-JADE Joint Diagonalization, and 3-mode Tensor HO-SVD.
Blind source separation achieved a +16.2 dB signal-to-interference ratio (SIR) gain.

Cite This Study

Artiom Kovnatsky (2026) studied this question.

synapsesocial.com/papers/6a801a1a75c2e31742c8693d https://doi.org/10.5281/zenodo.21922112

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Implication

Computational study demonstrates phase-rotor methods for matrix decomposition in numerical linear algebra, suggesting an alternative ontology for photonic hardware execution.

Phase Algebra: Matrices as Clifford Multivector Networks & Phase-Rotor Methods for SVD and Joint Diagonalization (An Extension of Linear Algebra) | (A Rust Prototype) | wAI ~ wErrors

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Implication

Key Points

Cite This Study

Phase Algebra: Matrices as Clifford Multivector Networks & Phase-Rotor Methods for SVD and Joint Diagonalization (An Extension of Linear Algebra) | (A Rust Prototype) | wAI ~ wErrors

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Implication

Key Points

Cite This Study

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