transformation
Let an agent explain transformations in mathematics, relay kinds and properties from mathematics sources, describe the named transformations, flag the database aliases, and distinguish transformations from functions generally, transforms as operators, decompositions in database theory and transformation in other senses such as biology or business.
Bundle → Layer → Finding → Questions Filled
4 bundles · 8 layers · 8 findings · 16 questions
Understand What a transformation is.
Definition
Definition.
Definition
Definition.
- What is a transformation, and how does it differ from functions, transforms and database decompositions? definition
- Is the question about geometry, analysis, signal processing or databases? boundary
Named
Named transformations.
Named
Named.
- What are homographies, sequence transformations, the inverse FFT and lossless and dependency preserving decompositions? definition
- Which entry fits the specific term? action
Geometry Geometric transformations.
Kinds
Kinds.
Kinds
Kinds.
- How do translations, rotations, affine and projective transformations differ? provenance
- Which references are standard? provenance
Groups
Transformation groups.
Groups
Groups.
- How did Klein s Erlangen program classify geometries by transformation groups? provenance
- Which sources are cited? provenance
Analysis Transforms and sequences.
Fourier
Fourier.
Fourier
Fourier.
- How do the Fourier transform and FFT work in signal processing? provenance
- Which entry fits fast Fourier transform? action
Sequences
Series acceleration.
Sequences
Sequences.
- How do sequence transformations such as Aitken s delta-squared accelerate convergence? provenance
- Which entry fits series acceleration? action
Context Other fields.
Databases
Decompositions.
Databases
Databases.
- What are lossless and dependency preserving decompositions in database normalisation? provenance
- Which entry fits database normalization? action
Vision
Computer vision.
Vision
Vision.
- How are homographies used in image stitching? provenance
- Which entry fits image stitching? action
Classifiers Filled
- Family
- Thing Registry
- Category
- Cross-cutting context
- Entry kind
- thing
- Plane
- XCT
- Domain
- XCT.QLT
- Other names and narrower kinds
- dependency preserving decomposition, lossless decomposition, sequence transform, inverse fast Fourier transformation, sequence transformation, homography, centering, projective transformation, Operational transformation, discrete transform, data transformation, polynomial transformation
What it is Filled
In mathematics, a transformation is a function from a set to itself, assigning each element of that set exactly one element of the same set; particular transformations may have additional geometric or algebraic properties, and an inverse transform is a mathematical mapping distinct from an algorithm used to compute it.
Why it exists Filled
Let an agent explain transformations in mathematics, relay kinds and properties from mathematics sources, describe the named transformations, flag the database aliases, and distinguish transformations from functions generally, transforms as operators, decompositions in database theory and transformation in other senses such as biology or business.
Distinguishing features Filled
- Maps structures
- Geometric and analytic kinds
- Composable
- Aliases include database terms
What robots and AI may and may not do Filled
Must not
- Confuse a transformation with a transform such as the Fourier transform without saying so.
- Apply transformations to data that silently distort it or lose information.
- Mix senses from database theory or other fields with the mathematical one.
Only with a human decision
- Applying transformations to datasets that feed decisions about people.
May
- Explain transformations in mathematics, such as geometric and projective ones, with examples.
- Apply transformations to data the agent is authorized to process.
Moral aspects Filled
- Transformed data can mislead if the transformation is hidden.
- Clear mathematics teaching helps students across sciences.
Who is affected
- Students
- Users of transformed data
- Analysts
Owners Filled
Steward
Nobody owns the concept; it belongs to mathematics as shared knowledge.
Links to other meta-models Filled
parent
- Q11348 - registry parent class
- Q24034552 - registry parent class
related
- function - in registry terms
- homography
- Fourier transform
- database normalization - for misfiled aliases
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.transformation-q12202238
- Wikidata: Q12202238 (https://www.wikidata.org/wiki/Q12202238)
Direct properties not applicable Not applicable
- fast Fourier transform: O(n log n) complexity
- homography: 3x3 matrix up to scale in the plane note
- registry parents: function, mathematical concept note
Plane XCT: no invented physical properties.
Recognition optional Filled
- Mapping of a set or space
- Homography, sequence transformation, inverse fast Fourier transformation, dependency preserving decomposition, lossless decomposition
- Functions are the general concept; transforms are operators on functions; database decompositions split relations
- Not a visible object; seen in diagrams of moved, scaled or distorted shapes.
Capabilities and actions required Filled
- explain the concept
- relay kinds and properties
- describe named transformations
- distinguish related senses
Hazards and failure modes required Filled
- Confusing transformation and transform
- Registry aliases from database theory
- Mixing mathematical and everyday senses
Standards and interfaces required Filled
- No regulation
Context of use required Filled
- Not applicable; a mathematical concept.
- geometric transformations such as isometries and homographies
- linear transformations
- integral transforms such as Fourier
- sequence transformations
- database decompositions as misfiled terms
Sources Filled
- Wikidata item Q12202238: transformation - identity and sense of the item
- Wikipedia: Transformation (function) - general description of the item
Open questions
- Should homography and sequence transformation be separate entries?
- How should mathematics sources be linked?
- The registry aliases dependency preserving decomposition and lossless decomposition should be moved to database normalization
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q12202238/spec.json