The Minimum-Norm Least Squares Solutions to Quaternion Tensor Systems
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Bibliographic record
Abstract
In this paper, we investigate the minimum-norm least squares solution to a quaternion tensor system A1*NX1=C1,A1*NX2+A2*NX3=C2,E1*NX1*MF1+E1*NX2*MF2+E2*NX3*MF2=D by using the Moore–Penrose inverses of block tensors. As an application, we discuss the quaternion tensor system A*NX=C,E*NX*MF=D for minimum-norm least squares reducible solutions. To illustrate the results, we present an algorithm and a numerical example.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it