genericSymmetricMatrix -- make a generic symmetric matrix

Synopsis

• Usage:

  genericSymmetricMatrix(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 symmetric matrix with n rows whose entries on and above the diagonal are the variables of R starting with r

Description

i1 : R = ZZ[a..z];

i2 : M = genericSymmetricMatrix(R,a,3)

o2 = | a b c |
     | b d e |
     | c e f |

             3       3
o2 : Matrix R  <--- R

i3 : transpose(M) - M == 0

o3 = true

i4 : genericSymmetricMatrix(R,d,5)

o4 = | d e f g h |
     | e i j k l |
     | f j m n o |
     | g k n p q |
     | h l o q r |

             5       5
o4 : Matrix R  <--- R

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

i5 : genericSymmetricMatrix(R,3)

o5 = | a b c |
     | b d e |
     | c e f |

             3       3
o5 : Matrix R  <--- R

i6 : genericSymmetricMatrix(R,5)

o6 = | a b c d e |
     | b f g h i |
     | c g j k l |
     | d h k m n |
     | e i l n o |

             5       5
o6 : Matrix R  <--- R

See also

• vars(Ring) -- row matrix of the variables
• genericMatrix -- make a generic matrix of variables
• genericSkewMatrix -- make a generic skew symmetric matrix of variables