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Research draft

matrix

vr.tr.matrix · INF.MED

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.

Thing Registry Information and virtual systems

Research draft, second pass

A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.

written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify

Researched by: Claude

Purpose and description

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.

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 are stored as array data structures in computing.

What it is for: Linear algebra, data representation and computation.

It can be perform matrix operations; explain properties such as rank, determinant and eigenvalues; apply matrices in transformations and systems; choose storage and algorithms in computing.

Distinguishing features

Rectangular array

Defined operations

Represents linear maps

Central to computation

What it looks like

Not physical; grids of numbers in brackets.

How it is recognised

Rows and columns

Dimensions m by n

A vector is a single row or column

Related models

is a kind of - category

array data structure

is a kind of - category

tensor

is related to - geometric transformations

line segment

is related to - covariance matrices

probability distribution

In practice

Families and kinds

square, diagonal and identity matrices

sparse and dense matrices

transformation and rotation matrices

payoff and adjacency matrices

generator and parity-check matrices in coding

Standards and regulation

ISO 80000-2 notation

Numerical library standards such as BLAS and LAPACK

Failure modes and hazards

Dimension mismatches

Numerical instability

Confusing senses of matrix

Also called

sparse matrixdense matrixcomplex conjugate matrixpayoff matrixtransformation matrixgenerator matrixrisk matrixco-occurrence matrixCauchy matrixfundamental matrixNext-generation matrixManin matrixrandom matrixstoichiometry matrixorthogonal arraygeneral matrixtranspose matrixFock matrixRosenbrock system matrixsimilarity matrixpolynomial matrixalternant matrixsubmatrixconfusion matrixsquare matrixtransfer function matrixquaternionic matrixparity-check matrixcommuting matricesgeneralized inverseParisi matrixZ-matrixJacobian matrixcompound matrixconformable matrixdata matrixdecomposition matrixdesign matrixdocument-term matrixray transfer matrix

+160

Where this came from

wikidata · CC0 1.0

Source repository Registry entry point

Also registered as vr.tr.matrix-artifact

Drafted structure

Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.

Compute Operations.

Rules of algebra.

Operations

Basic operations.

Operations

Operations.

  1. What is the product, inverse or transpose of these matrices? measurement
  2. Are the dimensions compatible? boundary

Properties

Key properties.

Properties

Properties.

  1. What are the rank, determinant and eigenvalues of this matrix? measurement
  2. What do they tell about the linear map? definition
Apply Applications.

Matrices everywhere.

Transform

Transformations.

Transform

Transformations.

  1. Which matrix represents this rotation, scaling or projection? definition
  2. How are transformations composed? definition

Systems

Linear systems.

Systems

Linear systems.

  1. How is this system of equations solved with matrices? action
  2. Is the system well-conditioned? boundary
Computing Storage and algorithms.

Efficiency matters.

Storage

Sparse and dense.

Storage

Storage.

  1. Should this matrix be stored as sparse or dense, and in which format? action
  2. How large is it? measurement

Numerics

Numerical stability.

Numerics

Numerics.

  1. Which algorithm and library should be used for this computation? action
  2. How can numerical error be controlled? action
Senses Disambiguation.

Matrix has other senses.

Other

Other meanings.

Other

Other meanings.

  1. Is a biological matrix, a material matrix, a payoff matrix in game theory or the film meant? boundary
  2. Which entry fits? action

Teach

Teaching.

Teach

Teaching.

  1. How can matrix operations be taught intuitively? action
  2. Which misconceptions arise? provenance

What the second pass must settle

  • Should each matrix type be a separate entry?
  • How should numerical libraries be linked?
  • How should other senses be split?
Draft as JSON