what is a supermatrix?


what is a supermatrix?

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In some sense, the name of a supermatrix is misleading, because the way in which it’s super has nothing to do with how good it is at being a matrix. Rather, it’s because they’re involved with explaining a concept in physics called “supersymmetry” and physicists call everything like that super (supermatrix, supervector, superalgebra, superfield, superspace…)

A supermatrix is like a normal matrix except that it has this concept of being “odd” or “even”, where this refers to how things multiply: the product of two odd supermatrices is odd, of two even is even, and of an odd and an even is even. Note that not all supermatrices are odd *or* even; these are called non-homogeneous supermatrices. There’s also a thing called supervectors which have a version of the odd/even thing, and supermatrices have the property that an odd supermatrix times an odd supervector results in an odd supervector, and an even supermatrix times an even or odd supervector results in an even supervector, and an odd supermatrix times an even supervector results in an even supervector.

This whole even/odd thing is a fundamental part of supersymmetry.