matrix concept
| Definition | A table of numbers with n rows and d columns that sends a vector to the linear combination of its columns with the vector's coordinates as the scalars. A data table with numeric columns is one. Primer L, equation L.5. |
|---|---|
| Example | Rows (2, 1) and (1, 3) send (1, 2) to 1 (2, 1) + 2 (1, 3) = (4, 7). |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id matrix, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | Book equation L.5. |
| Assumptions and scope | none |
| Prior art | none recorded |
| Evidence | none |
| Reviewed | semantic review 2026-09-09; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
Book equation L.5.
\[(Ax)_i=\sum_{j}A_{ij}x_j,\qquad Ax=x_1\,a_1+\cdots+x_d\,a_d\ \ \text{with } a_j \text{ the } j\text{th column}.\]
Conditions
none
Ledger
none
First stated
Primer L section L.3 of Data Mining as Observation, added in draft 0.3 (2026-09-09) for the ECE 514 readers whose first courses are far behind. The idea is standard and TSK Appendix A covers it at length.
Measurements
none
Failures and corrections
none
Invariance envelope
none declared
Machine checked
none
Used in
Data Mining as Observation primers L and S, chapters 0, 1, 4, 6, 7, 8, 9, 10, 12, 13.
Related
vector; transpose; inverse; rank; linear combination.
See also
none
Status
Generated 2026-09-10 by encyclopedia/generate.py; book
at observation-data-mining f3914f0; the commit of every record is listed
in the encyclopedia’s provenance.