# genericSkewMatrix -- make a generic skew symmetric matrix of variables

## Synopsis

• Usage:
genericSkewMatrix(R,r,n)
• Inputs:
• R, a ring
• r, , which is a variable in the ring R (this input is optional)
• n, an integer
• Outputs:
• a skew symmetric matrix with n rows whose entries above the diagonal are the variables of R starting with r

## Description

A square matrix M is skew symmetric if transpose(M) + M == 0.
 i1 : R = ZZ[a..z]; i2 : M = genericSkewMatrix(R,a,3) o2 = | 0 a b | | -a 0 c | | -b -c 0 | 3 3 o2 : Matrix R <--- R i3 : transpose(M) + M == 0 o3 = true i4 : genericSkewMatrix(R,d,5) o4 = | 0 d e f g | | -d 0 h i j | | -e -h 0 k l | | -f -i -k 0 m | | -g -j -l -m 0 | 5 5 o4 : Matrix R <--- R

Omitting the input r is the same as having r be the first variable in R.

 i5 : genericSkewMatrix(R,3) o5 = | 0 a b | | -a 0 c | | -b -c 0 | 3 3 o5 : Matrix R <--- R i6 : genericSkewMatrix(R,5) o6 = | 0 a b c d | | -a 0 e f g | | -b -e 0 h i | | -c -f -h 0 j | | -d -g -i -j 0 | 5 5 o6 : Matrix R <--- R