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Macaulay2Doc :: genericSkewMatrix

genericSkewMatrix -- make a generic skew symmetric matrix of variables

Synopsis

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

See also

Ways to use genericSkewMatrix :