read direction concept
| Definition | An eigenvector of the read operator with a nonzero eigenvalue, a direction the consumer is sensitive to. Chapter 2 section 2.2. |
|---|---|
| Example | For the consumer 3x1 + 4x2 the read direction is (3, 4) over 5. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id read-direction, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | none |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | lean/DataMiningAsObservation/ReadOperator.lean, lean/DataMiningAsObservation/Projection.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
none
Conditions
- An eigenvector of the read operator with a nonzero eigenvalue, a direction the consumer is sensitive to. An affine consumer has exactly one, its weight vector, the projection onto a read direction is idempotent, and its residual is orthogonal to it.
- The code that puts the whole error on the read direction is the worst, the control that destroys the read direction is confirmed worst, and no code of a given total error can be read as more than the total.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Chapter 2 section 2.2 and chapter 4 section 4.3 of Data Mining as
Observation, with the control that destroys the read direction in
geometric-observation/chapters/ch08_value.md:40-70.
Measurements
none
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/ReadOperator.lean,
theorems rank_one_reads_one_direction,
readOp_mulVec, quad_readOp,
quad_readOp_nonneg, readOp_mulVec_eq_zero_iff,
readOp_diag, readOp_offdiag,
readOp_symm, readOp_neg,
affine_const_along_nuisance, readOp_affine,
readOp_sqLength_basis, at observation-data-mining f3914f0;
what the check covers is stated in the book’s appendix
C.
lean/DataMiningAsObservation/Projection.lean,
theorems proj_proj, dot_sub_proj,
proj_sq_le, proj_add_orth,
proj_add, at observation-data-mining f3914f0; what the
check covers is stated in the book’s appendix
C.
Used in
Data Mining as Observation chapters 2, 3, 4, 6, 8, 11, 12.
Related
read subspace; read operator; sensitivity; nuisance; projection.
See also
Book equations stated beside the entry’s terms, not defining it: 0.9, 6.1, 4.2.
Ledger rows that cite the entry’s records without naming it: GO-1, GO-2 (pos. half: consumer-projected covariance controls).
Sources-table rows that share a record with the entry without naming it: chapter 1 section 1.4, chapter 4 section 4.3, chapter 6 section 6.2, chapter 11 section 11.7.
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.