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 :

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

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But now it is a symmetric matrix:

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Out[3]=

Scope  (1)

Applications  (3)

Properties & Relations  (3)

Possible Issues  (2)

See Also

Arrays  Vectors  MatrixQ  TensorRank  TensorDimensions  TensorSymmetry

Tutorials

Introduced in 2012
(9.0)