Manuals/calci/ANTIDIAGONAL

MATRIX (TypeOfMatrix,DimensionsOfMatrix,SeedValuesToUse,IJFunction,PreParameter,IsItInternalCall)

• $TypeOfMatrix$ is the type of the matrix.
• $DimensionsOfMatrix$ is the order of the Anti diagonal matrix.

Description

• This function gives the matrix satisfying the anti diagonal properties.
• 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.
• So here we are getting all entries are 0 except from the opposite of main diagonal as 1.
• 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.
• To display the different order of matrices then the syntax is MATRIX("anti-diagonal",5).

Examples

• MATRIX("ANTI-DIAGONAL") = 1
• MATRIX("ANTI-DIAGONAL",3)

0	0	1
0	1	0
1	0	0

• MATRIX("anti-diagonal",4,200..204)

0	0	0	200
0	0	201	0
0	202	0	0
203	0	0	0

• MATRIX("anti-diagonal",3,-32.05)

0	0	-32.05
0	-32.05	0
-32.05	0	0

See Also

• ARROWHEAD
• MATRIXOPERATORS

References

• Anti Diagonal

• List of Main Z Functions

• Z3 home