# Matrices

Matrices[{d1,d2}]

represents the domain of matrices of dimensions d1×d2.

Matrices[{d1,d2},dom]

represents the domain of matrices of dimensions d1×d2, with components in the domain dom.

Matrices[{d1,d2},dom,sym]

represents the subdomain of matrices d1×d2 with symmetry sym.

# Details

• Valid dimension specifications di in Matrices[{d1,d2},dom,sym] are positive integers. It is also possible to work with symbolic dimension specifications.
• Valid component domain specifications dom are either Reals or Complexes. Matrices[{d1,d2}] uses Complexes by default.
• For matrices, the symmetry sym can be either Symmetric[{1,2}], Antisymmetric[{1,2}], or {}, which represents the trivial symmetry.
• If the symmetry sym is nontrivial, then the dimensions d1 and d2 must coincide.

# Examples

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## Basic Examples(1)

An antisymmetric real matrix in dimension :

 In[1]:=
 Out[1]=

The Dot product of with itself is also a × matrix:

 In[2]:=
 Out[2]=

But now it is a symmetric matrix:

 In[3]:=
 Out[3]=