BUILT-IN MATHEMATICA SYMBOL

# SymmetrizedArray

SymmetrizedArray[{pos1->val1, pos2->val2, ...}, dims, sym]
yields an array of dimensions dims whose entries are given by those in the rules or through the symmetry sym.

SymmetrizedArray[list]
yields a symmetrized array version of list.

## DetailsDetails

• SymmetrizedArray takes unspecified elements to be 0.
• SymmetrizedArray[data, ...] is converted to an expression of the form StructuredArray[SymmetrizedArray, dims, structureddata], where structureddata contains the symmetry and independent component rules corresponding to the input.
• Normal[SymmetrizedArray[...]] gives the ordinary array corresponding to a symmetrized array object.
• SymmetrizedArrayRules[SymmetrizedArray[...]] gives the list of independent rules .
• ArrayRules[SymmetrizedArray[...]] gives the list of both dependent and independent rules .
• The elements in a SymmetrizedArray object need not be numeric.
• The position specifications can contain patterns.
• With rules , the are evaluated separately for each independent component that matches .
• SymmetrizedArray[list] requires that list be a full array, with all parts at a particular level being lists of the same length.
• The individual elements of a symmetrized array cannot themselves be lists.
• SymmetrizedArray[rules] yields a symmetrized array, with dimensions exactly large enough to include elements whose positions have been explicitly specified.
• StructuredArray[SymmetrizedArray, ...] is treated as a raw object by functions like AtomQ and for purposes of pattern matching.

## ExamplesExamplesopen allclose all

### Basic Examples (2)Basic Examples (2)

Construct an antisymmetric array:

 Out[1]=

Convert it to an ordinary matrix:

 Out[2]=

Convert an array with symmetry into its symmetrized form:

 Out[1]=

These are its independent components:

 Out[2]=