# Matrix ** RingElement -- a binary operator, usually used for tensor product or Cartesian product

## Synopsis

• Operator: **
• Usage:
f ** r
• Inputs:
• f,
• r,
• Outputs:
• the tensor product of f with r

## Description

 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