Frobenius norm concept
| Definition | The square root of the sum of a matrix's squared entries, which also equals the square root of the sum of its squared singular values. The error of a low-rank approximation is measured in it. Primer L, equation L.18. Also Frobenius. |
|---|---|
| Example | Rows (1, 1), (1, 0), and (0, 1) have squared Frobenius norm 4, which is 3 + 1. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id frobenius-norm, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | Book equation L.18. |
| 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.18.
\[\|A\|_F^{2}=\sum_{i,j}A_{ij}^{2}=\sum_i\sigma_i^{2},\qquad \min_{\operatorname{rank}B\le k}\|A-B\|_F^{2}=\sum_{i>k}\sigma_i^{2}.\]
Conditions
none
Ledger
none
First stated
Primer L section L.8 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.
Related
singular value; low-rank approximation; length, norm.
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.