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determinant -- determinant of a matrix

Synopsis

Usage:
det M
Inputs:
- M, a square matrix
Outputs:
- a ring element, which is the determinant of M
Optional inputs:
- Strategy => ..., -- choose between Bareiss and Cofactor algorithms

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

Ways to use `determinant` :

determinant(Matrix)