linear combination concept
| Definition | A sum of scalar multiples of vectors. A matrix sends a vector to the linear combination of its columns with the vector's coordinates as the scalars. Primer L, equations L.1 and L.5. |
|---|---|
| Example | 2(1, 2) + (3, -1) = (5, 3). |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id linear-combination, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | Book equation L.1. |
| 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.1.
\[x+y=(x_1+y_1,\dots,x_d+y_d),\qquad c\,x=(c\,x_1,\dots,c\,x_d).\]
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.1 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
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Failures and corrections
none
Invariance envelope
none declared
Machine checked
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Used in
Data Mining as Observation primer L.
Related
See also
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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.