genericSkewMatrix -- make a generic skew symmetric matrix of variables

Usage:

genericSkewMatrix(R,r,n)
Inputs:
- R, a ring
- r, a ring element, 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

Ways to use genericSkewMatrix:

genericSkewMatrix(Ring,RingElement,ZZ)
genericSkewMatrix(Ring,ZZ)

For the programmer

The object genericSkewMatrix is a method function.

The source of this document is in Macaulay2Doc/functions/genericSkewMatrix-doc.m2:36:0.

genericSkewMatrix -- make a generic skew symmetric matrix of variables

Description

See also

Ways to use genericSkewMatrix:

For the programmer