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Diagonal matrix

In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices. Elements of the main diagonal can either be zero or nonzero. An example of a 2×2 diagonal matrix is [ 3 0 0 2 ] {\displaystyle \left[{\begin{smallmatrix}3&0\\0&2\end{smallmatrix}}\right]} , while an…

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Overview

Definition

Vector-to-matrix diag operator

Scalar matrix

Vector operations

Matrix operations

Operator matrix in eigenbasis

Properties

Applications

Operator theory

Sources

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Diagonal matrix

Nodes83
Edges82
Triples31
Avg. degree1.98
Density0.024096
Components1

How this topic connects Entity context

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Diagonal matrix

Top relations

related to Scalar matrix · 8
Diagonal matrix → By, Diagonal, DM, For, Its, MD, That, The
has application · 4
Diagonal matrix → Because, Diagonal, In, Such
related to Vector operations · 4
Diagonal matrix → Given, Hadamard, Multiplying, This
is a · 3
Diagonal matrix → matrix in which all off-diagonal entries are zero, matrix in which the entries outside the main diagonal are all zero, symmetric matrix
related to Definition · 3
Diagonal matrix → As, However, That
related to Matrix operations · 3
Diagonal matrix → The, Then, Write
related to Properties · 3
Diagonal matrix → In, The, Where
see also · 2
Diagonal matrix → Anti-diagonal, Lie
related to Vector-to-matrix diag operator · 1
Diagonal matrix → This

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Important terminology

matrix diagonal displaystyle diag matrices end vector operatorname entries mathbf begin scalar zero algebra operator square bmatrix multiplication left dots

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Diagonal matrixis amatrix in which the entries outside the main diagonal are all zero0.90text
Diagonal matrixis amatrix in which all off-diagonal entries are zero0.90text
Diagonal matrixis asymmetric matrix0.90text
Diagonal matrixhas applicationDiagonal0.60section
Diagonal matrixhas applicationBecause0.60section
Diagonal matrixhas applicationIn0.60section
Diagonal matrixhas applicationSuch0.60section
Diagonal matrixrelated to DefinitionAs0.60section
Diagonal matrixrelated to DefinitionThat0.60section
Diagonal matrixrelated to DefinitionHowever0.60section
Diagonal matrixrelated to Matrix operationsThe0.60section
Diagonal matrixrelated to Matrix operationsWrite0.60section

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