Manuals/calci/MONOMIAL

MATRIX("MONOMIAL",order)

• $order$ is the order of the Monomial matrix.

Description

• This function gives the matrix of order 3 with the property of monomial matrix.
• A monomial matrix is a square matrix with exactly one nonzero entry in each row and exactly one nonzero entry in each column.
• So here MATRIX("monomial") is showing the monomial matrix of order 3.
• Monomial matrix is also called as generalized permutation matrix.
• So in Calci, users can give the argument as MATRIX("Monomial") or MATRIX(" generalized permutation").
• An example of monomial or generalized permutation matrix is:

${\begin{bmatrix}0&0&3&0\\0&-2&0&0\\4&0&0&0\\0&0&0&1\\\end{bmatrix}}$

• So any monomial matrix is the product of a permutation matrix and a diagonal matrix.

Examples

• 1.MATRIX("Monomial")=1
• 2.MATRIX("Monomial",3)

0	0	3
2	0	0
0	1	0

• 3.MATRIX("Generalized permutation",3)

0	3	0
3	0	0
0	0	2

• 4.MATRIX("generalized permutation",5,-10..-2)

0	0	0	-10	0
0	-9	0	0	0
0	0	-8	0	0
0	0	0	0	-7
-6	0	0	0	0

See Also

• HADAMARD
• EXCHANGE
• IDENTITY
• HANKEL

References

• Generalized Permutation Matrix