matrix
Let an agent explain matrices and their operations, perform and check matrix computations, apply matrices in science, engineering and computing, and separate other senses of matrix.
Bundle → Layer → Finding → Questions Filled
4 bundles · 8 layers · 8 findings · 16 questions
Compute Operations.
Operations
Basic operations.
Operations
Operations.
- What is the product, inverse or transpose of these matrices? measurement
- Are the dimensions compatible? boundary
Properties
Key properties.
Properties
Properties.
- What are the rank, determinant and eigenvalues of this matrix? measurement
- What do they tell about the linear map? definition
Apply Applications.
Transform
Transformations.
Transform
Transformations.
- Which matrix represents this rotation, scaling or projection? definition
- How are transformations composed? definition
Systems
Linear systems.
Systems
Linear systems.
- How is this system of equations solved with matrices? action
- Is the system well-conditioned? boundary
Computing Storage and algorithms.
Storage
Sparse and dense.
Storage
Storage.
- Should this matrix be stored as sparse or dense, and in which format? action
- How large is it? measurement
Numerics
Numerical stability.
Numerics
Numerics.
- Which algorithm and library should be used for this computation? action
- How can numerical error be controlled? action
Senses Disambiguation.
Other
Other meanings.
Other
Other meanings.
- Is a biological matrix, a material matrix, a payoff matrix in game theory or the film meant? boundary
- Which entry fits? action
Teach
Teaching.
Teach
Teaching.
- How can matrix operations be taught intuitively? action
- Which misconceptions arise? provenance
Classifiers Filled
- Family
- Thing Registry
- Category
- Information and virtual systems
- Entry kind
- thing
- Plane
- INF
- Domain
- INF.MED
- Other names and narrower kinds
- sparse matrix, dense matrix, complex conjugate matrix, payoff matrix, transformation matrix, generator matrix, risk matrix, co-occurrence matrix, Cauchy matrix, fundamental matrix, Next-generation matrix, Manin matrix
What it is Filled
A rectangular array of numbers, symbols or expressions arranged in rows and columns, used to represent linear transformations, systems of equations, graphs, games and data, with operations such as addition, multiplication, transposition and inversion; matrices include special types such as sparse, transformation, payoff and generator matrices and can be represented in computing using array data structures, sparse formats or other representations.
Why it exists Filled
Let an agent explain matrices and their operations, perform and check matrix computations, apply matrices in science, engineering and computing, and separate other senses of matrix.
Distinguishing features Filled
- Rectangular array
- Defined operations
- Represents linear maps
- Central to computation
What robots and AI may and may not do Filled
Must not
- Present a numerically unstable result as accurate.
- Hide errors in matrix computations behind models that affect people's lives, such as credit scoring.
Only with a human decision
- Using matrix-based models for decisions about people.
May
- Compute with matrices and report results with stated precision.
- Explain matrix operations and their uses.
Moral aspects Filled
- Opaque models built on matrices can encode bias in decisions about people.
- Mathematics teaching should be accurate and accessible.
Who is affected
- Students
- People affected by models
- Engineers relying on computations
Owners Filled
Steward
Nobody: an abstract concept held in common.
Links to other meta-models Filled
parent
- Q186152 - registry parent class
- Q188524 - registry parent class
related
- array data structure - category
- tensor - category
- line segment - geometric transformations
- probability distribution - covariance matrices
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.matrix
- Wikidata: Q44337 (https://www.wikidata.org/wiki/Q44337)
Direct properties not applicable Not applicable
Not applicable
Plane INF: no invented physical properties.
Recognition optional Filled
- Rows and columns
- Dimensions m by n
- A vector is a single row or column
- Not physical; grids of numbers in brackets.
Capabilities and actions required Filled
- perform matrix operations
- explain properties such as rank, determinant and eigenvalues
- apply matrices in transformations and systems
- choose storage and algorithms in computing
Hazards and failure modes required Filled
- Dimension mismatches
- Numerical instability
- Confusing senses of matrix
Standards and interfaces required Filled
- ISO 80000-2 notation
- Numerical library standards such as BLAS and LAPACK
Context of use required Filled
- Linear algebra, data representation and computation.
- square, diagonal and identity matrices
- sparse and dense matrices
- transformation and rotation matrices
- payoff and adjacency matrices
- generator and parity-check matrices in coding
Sources Filled
- Wikidata item Q44337: matrix - identity and sense of the item
- Wikipedia: Matrix (mathematics) - general description of the item
Open questions
- Should each matrix type be a separate entry?
- How should numerical libraries be linked?
- How should other senses be split?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q44337/spec.json