antihermitian - Maple Help

The antihermitian Indexing Function

Description

 • The antihermitian indexing function can be used to construct rtable objects of type Array or Matrix.
 • In the construction of 2-dimensional objects, the antihermitian indexing function specifies that the (i, j)th element is equal to the negative of the complex conjugate of the (j, i)th element.
 The name skewhermitian is equivalent to antihermitian.

Examples

 > $M≔\mathrm{Matrix}\left(1..3,1..3,\mathrm{shape}=\mathrm{antihermitian}\right)$
 ${M}{≔}\left[\begin{array}{ccc}{0}& {0}& {0}\\ {0}& {0}& {0}\\ {0}& {0}& {0}\end{array}\right]$ (1)
 > $M\left[1,2\right]≔1+2I$
 ${{M}}_{{1}{,}{2}}{≔}{1}{+}{2}{}{I}$ (2)
 > $M$
 $\left[\begin{array}{ccc}{0}& {1}{+}{2}{}{I}& {0}\\ {-1}{+}{2}{}{I}& {0}& {0}\\ {0}& {0}& {0}\end{array}\right]$ (3)
 > $A≔\mathrm{Array}\left(\mathrm{skewhermitian},1..4,1..4,\left(a,b\right)↦a+I\cdot a\cdot b\right)$
 ${A}{≔}\left[\begin{array}{cccc}{0}& {1}{+}{2}{}{I}& {1}{+}{3}{}{I}& {1}{+}{4}{}{I}\\ {-1}{+}{2}{}{I}& {0}& {2}{+}{6}{}{I}& {2}{+}{8}{}{I}\\ {-1}{+}{3}{}{I}& {-2}{+}{6}{}{I}& {0}& {3}{+}{12}{}{I}\\ {-1}{+}{4}{}{I}& {-2}{+}{8}{}{I}& {-3}{+}{12}{}{I}& {0}\end{array}\right]$ (4)