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Matrix / Number -- scalar division

Synopsis

Operator: /
Usage:

v / c
Inputs:
- v, a matrix or a vector,
- c, a number or a ring element,
Outputs:
- a matrix or a vector,

Description

This operation is equivalent to right scalar multiplication by the multiplicative inverse of c, i.e., v * (1/c).

i1 : R = QQ[a,b,c,d]

o1 = R

o1 : PolynomialRing

i2 : matrix {{d, -b}, {-c, a}} / (a * d - b * c)

o2 = | (-d)/(bc-ad) b/(bc-ad)    |
     | c/(bc-ad)    (-a)/(bc-ad) |

                    2             2
o2 : Matrix (frac R)  <-- (frac R)

Caveat

The base ring of the output will be a field containing the base ring of v.

Ways to use this method:

Matrix / Number -- scalar division
Matrix / RingElement
Vector / Number
Vector / RingElement