Bibliographic record
Abstract
In this chapter, the authors review some of the basic results from the theory of matrices and determinants. They denote by Mat<sub><i>m×n</i></sub> the set of <i>m×n</i> matrices (that is, <i>m</i> rows and <i>n</i> columns) with real entries. When <i>m = n</i>, they say that the matrices are square. It is easily shown that with the usual matrix addition and scalar multiplication, Mat<sub><i>m×n</i></sub> is a vector space, and that with the usual matrix multiplication, Mat<sub><i>m×m</i></sub> is a ring. Multi-index notation provides a convenient way to specify submatrices of matrices. Matrices have many desirable computational properties. For this reason, when computing in vector spaces, it is often convenient to reformulate arguments in terms of matrices. The chapter discusses the row rank and column rank of matrices. It defines the trace and determinant of a matrix and extends these concepts to linear maps.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
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 | 0.000 | 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) | 0.004 | 0.000 |
Machine scores (provisional)
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".