i1 : f = matrix "2,3,4;5,6,7"
o1 = | 2 3 4 |
| 5 6 7 |
2 3
o1 : Matrix ZZ <--- ZZ
|
i2 : f ** 10
o2 = | 20 30 40 |
| 50 60 70 |
2 3
o2 : Matrix ZZ <--- ZZ
|
When the ring element is homogeneous, the degrees of the source module can change, which is what makes this operation different from scalar multiplication.
i3 : QQ[x,y] o3 = QQ[x..y] o3 : PolynomialRing |
i4 : f = matrix "x,y"
o4 = | x y |
1 2
o4 : Matrix (QQ[x..y]) <--- (QQ[x..y])
|
i5 : g = f ** y^7
o5 = | xy7 y8 |
1 2
o5 : Matrix (QQ[x..y]) <--- (QQ[x..y])
|
i6 : h = f * y^7
o6 = | xy7 y8 |
1 2
o6 : Matrix (QQ[x..y]) <--- (QQ[x..y])
|
i7 : degrees g
o7 = {{{0}}, {{8}, {8}}}
o7 : List
|
i8 : degrees h
o8 = {{{0}}, {{1}, {1}}}
o8 : List
|