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Invertible matrix

In linear algebra, an invertible matrix (non-singular, non-degenerate or regular) is a square matrix that has an inverse. In other words, if a matrix is invertible, it can be multiplied by its inverse matrix to yield the identity matrix. Invertible matrices are the same size as their inverse.

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Overview

Definition

Basic idea

Examples

Criteria for invertibility

Methods of matrix inversion

Properties

Derivative of the matrix inverse

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Applications

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Invertible matrix

Nodes93
Edges92
Triples29
Avg. degree1.98
Density0.021505
Components1

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Invertible matrix

Top relations

related to Invertible matrix theorem · 11
Invertible matrix → AB, AT, Ax, BA, In, Kn, Let, More, Similarly, The, There
related to Other properties · 11
Invertible matrix → AB, AR, Ax, For, Furthermore, LA, Left, Moore, More, Penrose, That
related to Derivative of the matrix inverse · 3
Invertible matrix → Suppose, Then, To
related to Diagonalization · 3
Invertible matrix → An, Matrix, This

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Important terminology

matrix inverse invertible displaystyle matrices mathbf identity linear determinant -1 rank square n-by-n set right vector equivalently form singular left

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
the real numbersinstance ofover a field0.80text
Invertible matrixrelated to Derivative of the matrix inverseSuppose0.60section
Invertible matrixrelated to Derivative of the matrix inverseThen0.60section
Invertible matrixrelated to Derivative of the matrix inverseTo0.60section
Invertible matrixrelated to DiagonalizationMatrix0.60section
Invertible matrixrelated to DiagonalizationAn0.60section
Invertible matrixrelated to DiagonalizationThis0.60section
Invertible matrixrelated to Invertible matrix theoremLet0.60section
Invertible matrixrelated to Invertible matrix theoremThe0.60section
Invertible matrixrelated to Invertible matrix theoremAB0.60section
Invertible matrixrelated to Invertible matrix theoremIn0.60section
Invertible matrixrelated to Invertible matrix theoremBA0.60section

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