congruenceDiagonalize -- diagonalizing a symmetric matrix via congruence

Synopsis

• Usage:

  congruenceDiagonalize(M)

• Inputs:
  • M, a matrix, a symmetric matrix over any field
• Outputs:
  • a matrix, a diagonal matrix congruent to M

Description

Given a symmetric matrix $M$ over any field, this command gives a diagonal matrix congruent to $M$. Note that the order in which the diagonal terms appear is not specified.

i1 : M=matrix(GF(17), {{7, 9}, {9, 6}});

                   2            2
o1 : Matrix (GF 17)  <-- (GF 17)

i2 : congruenceDiagonalize(M)

o2 = | 7 0  |
     | 0 -8 |

                   2            2
o2 : Matrix (GF 17)  <-- (GF 17)

See also

• diagonalClass -- produces a diagonalized form for any Grothendieck-Witt class, with simplified terms on the diagonal