determinant -- determinant of a matrix

Synopsis

• Usage:

  det M

• Inputs:
  • M, a square matrix
• Optional inputs:
  • Strategy => ..., default value null, choose between Bareiss, Cofactor and Dynamic algorithms
• Outputs:
  • a ring element, which is the determinant of M

Description

i1 : R = QQ[vars(0..8)]

o1 = R

o1 : PolynomialRing

i2 : M = genericMatrix(R,2,2)

o2 = | a c |
     | b d |

             2      2
o2 : Matrix R  <-- R

i3 : det M

o3 = - b*c + a*d

o3 : R

i4 : N = genericMatrix(R,3,3)

o4 = | a d g |
     | b e h |
     | c f i |

             3      3
o4 : Matrix R  <-- R

i5 : det N

o5 = - c*e*g + b*f*g + c*d*h - a*f*h - b*d*i + a*e*i

o5 : R

See also

• exteriorPower -- exterior power
• minors -- ideal generated by minors
• permanents -- ideal generated by square permanents of a matrix
• pfaffians -- ideal generated by Pfaffians