determinant concept
| Definition | For a two by two matrix, ad minus bc, the number whose vanishing means the columns are dependent and no inverse exists. For a symmetric matrix it is the product of the eigenvalues. Primer L, equation L.6. |
|---|---|
| Example | Rows (1, 2) and (2, 4) give 4 - 4 = 0, so the matrix has no inverse. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id determinant, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | Book equation L.6. |
| 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.6.
\[A=\begin{pmatrix}a&b\\ c&d\end{pmatrix},\qquad \det A=ad-bc,\qquad A^{-1}=\frac{1}{ad-bc}\begin{pmatrix}d&-b\\ -c&a\end{pmatrix}.\]
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 primer L, chapters 2.
Related
inverse; rank; eigenvalue, eigenvector; linear independence.
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.