genericSymmetricMatrix -- make a generic symmetric matrix

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

A square matrix M is symmetric if transpose(M) - M == 0.

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

Ways to use genericSymmetricMatrix:

genericSymmetricMatrix(Ring,RingElement,ZZ)
genericSymmetricMatrix(Ring,ZZ)

For the programmer

The object genericSymmetricMatrix is a method function.

The source of this document is in Macaulay2Doc/functions/genericSymmetricMatrix-doc.m2:37:0.

genericSymmetricMatrix -- make a generic symmetric matrix

Description

See also

Ways to use genericSymmetricMatrix:

For the programmer