Hey everyone... can some one explain to me why a vertical shear of 5 is NOT
1 0
0 5
thanks!
Well the general form for a vertical shear is
1 0
m 1
but you can also tell by multiplying it by the basis vectors.
[[1,0],[0,5]]*[1,0]=[1,0]
so you see the (1,0) vector does not change in the transformation, which should not be the case in a vertical shear. What this actually does is stretch everything out, because as you can see any y value is multiplied by 5, where in a shear transformation the magnitude of the y value changes according to the x value.
Thats correct.
think about how something in a vertical sheer moves. It moves vertically, but the magnatitude of that movement is determined by its horizontal position (the farther it's x value is from zero the more its y value changes)
so [[1,0],[5,1]]*[x,y] = [x,(5*x+y)]
so while you could say 5 is in the 'x collumn', because it is multiplied by x, it is in the 'y row', because that product is added to y*1 to become the new y value.