Manuals/calci/ANTIDIAGONALWITH

ANTIDIAGONALWITH()

• Parameter can be any Matrix.

Description

• This function gives the matrix satisfying the anti diagonal properties also it is replacing the constant given number in the anti diagonal entries.
• An anti-diagonal matrix is a matrix where all the entries are zero except those on the diagonal going from the lower left corner to the upper right corner ($\nearrow$), known as the anti-diagonal.
• The properties of anti diagonal matrix are:
• 1.The product of two anti-diagonal matrices is a diagonal matrix.
• 2. If A and D are n×n anti-diagonal and diagonal matrices, respectively, then AD,DA are anti-diagonal.
• 3.All anti-diagonal matrices are also persymmetric.

Examples

1. ANTIDIAGONALWITH([[1,2],[3,4]],34)

${\begin{matrix}1&34\\34&4\end{matrix}}$

1. ANTIDIAGONALWITH([[6,12,10,16],[13,14,15,17],[5,13,19,20],[3,24,33,43]],-22)

${\begin{matrix}6&12&10&-22\\13&14&-22&17\\5&-22&19&20\\-22&24&33&43\end{matrix}}$

See Also

• ANTIDIAGONAL
• ARROWHEAD
• MATRIXOPERATORS

References

• Anti Diagonal

• List of Main Z Functions

• Z3 home