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Supermatrix

In mathematics and theoretical physics, a supermatrix is a Z2-graded analog of an ordinary matrix. Specifically, a supermatrix is a 2×2 block matrix with entries in a superalgebra (or superring). The most important examples are those with entries in a commutative superalgebra (such as a Grassmann algebra) or an ordinary field (thought of as a purely even…

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Overview

Definitions and notation

Algebraic structure

As linear transformations

Operations

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Map overview Semantic statistics

Supermatrix

Nodes39
Edges38
Triples45
Avg. degree1.95
Density0.051282
Components1

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Supermatrix

Top relations

related to As linear transformations · 8
Supermatrix → General, If, Likewise, Odd, Ordinary, Such, The, There
related to Algebraic structure · 7
Supermatrix → In, Let Mr, Mr, One, Supermatrices, These, This
is a · 5
Supermatrix → new operation without an ungraded analog, Z2-graded analog of an ordinary matrix, Z2-graded analog of the determinant, Z2-graded analog of the trace, Z2-graded analog of the transpose
related to Berezinian · 4
Supermatrix → In, R0, The Berezinian, Z2-graded
related to Multiplication · 4
Supermatrix → Note, One, The, XY
related to Scalar multiplication · 4
Supermatrix → Left, Let, Scalar, This
related to Addition · 3
Supermatrix → It, The, Two
related to Supertrace · 3
Supermatrix → It, The, Z2-graded
related to Supertranspose · 3
Supermatrix → Let, The, Z2-graded
related to Definitions and notation · 2
Supermatrix → Let, Often

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Important terminology

supermatrices even ordinary odd ungraded matrix superalgebra homogeneous multiplication transpose one case parity linear elements square supertranspose dimension blocks block

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Supermatrixis aZ2-graded analog of an ordinary matrix0.90text
Supermatrixis aZ2-graded analog of the transpose0.90text
Supermatrixis anew operation without an ungraded analog0.90text
Supermatrixis aZ2-graded analog of the trace0.90text
Supermatrixis aZ2-graded analog of the determinant0.90text
Supermatrixrelated to AdditionTwo0.60section
Supermatrixrelated to AdditionThe0.60section
Supermatrixrelated to AdditionIt0.60section
Supermatrixrelated to Algebraic structureSupermatrices0.60section
Supermatrixrelated to Algebraic structureThese0.60section
Supermatrixrelated to Algebraic structureOne0.60section
Supermatrixrelated to Algebraic structureLet Mr0.60section

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