Supermatrix

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a> and <a href="/facts/Theoretical_physics/Cs2Y12rQ">theoretical physics</a>, a supermatrix is a Z2-graded analog of an ordinary <a href="/facts/Matrix_(mathematics)/qa8FI4ko">matrix</a>. Specifically, a supermatrix is a 2×2 <a href="/facts/Block_matrix/fPI8HX9f">block matrix</a> with entries in a <a href="/facts/Superalgebra/96vSHP12">superalgebra</a> (or <a href="/facts/Superring/96vSHP12">superring</a>). The most important examples are those with entries in a <a href="/facts/Commutative_superalgebra/crvGwsXC">commutative superalgebra</a> (such as a <a href="/facts/Grassmann_algebra/rdN4TvpR">Grassmann algebra</a>) or an ordinary <a href="/facts/Field_(mathematics)/xAjAS4ko">field</a> (thought of as a purely even commutative superalgebra).
</p><p>Supermatrices arise in the study of <a href="/facts/Super_linear_algebra/JW8jElFE">super linear algebra</a> where they appear as the coordinate representations of a <a href="/facts/Linear_transformation/Q1PBKNVV">linear transformations</a> between finite-dimensional <a href="/facts/Super_vector_space/JW8jElFE">super vector spaces</a> or free <a href="/facts/Supermodule/Q7kBorQo">supermodules</a>. They have important applications in the field of <a href="/facts/Supersymmetry/hkWGrMet">supersymmetry</a>.
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Supermatrix open-in-new

Supermatrix