- #1
nigelscott
- 135
- 4
H is a contravariant transformation matrix, M is a covariant transformation matrix, G is the metric tensor and G-1 is its inverse. Consider an oblique coordinates system with angle between the axes = α
I have G = 1/sin2α{(1 -cosα),(-cosα 1)} <- 2 x 2 matrix
I compute H = G*M where M = {(1 0), (cosα sinα)} and get H = {(1 -1/tanα),(0 1/sina)} which is what I expect.
Now I want go from H back to M so I compute M = G-1H
So by my reckoning G-1 = 1/sin4α{(1 cosα),(cosα 1)}
But when I multiply G-1 and H I don't get back to M. The is a 1/sin4α multiplying the whole thing.
What am I missing?
I have G = 1/sin2α{(1 -cosα),(-cosα 1)} <- 2 x 2 matrix
I compute H = G*M where M = {(1 0), (cosα sinα)} and get H = {(1 -1/tanα),(0 1/sina)} which is what I expect.
Now I want go from H back to M so I compute M = G-1H
So by my reckoning G-1 = 1/sin4α{(1 cosα),(cosα 1)}
But when I multiply G-1 and H I don't get back to M. The is a 1/sin4α multiplying the whole thing.
What am I missing?