Recent content by bohdy

Excellent. That's the kind of solution I was hoping for. Many thanks.

Hi, Can you elaborate on how to construct Tinverse easily? Isn't the computational difficulty the same, in that finding T such that T.v=w is as hard as finding a Tinv such that Tinv.w=v? Any matrix will do. I will then be applying the transformation to other vectors in the space (I...

I'm looking to map Rn to Rn. See above post. I used the 3D vector (1,1,1) as an example. ...so in R7 I want to map (1,1,1,1,1,1,1) to (0,0,0,0,0,0,1) etc.

In 2D: T= {{1, -1}, {1, 0}} Tinverse = {{0, 1}, {-1, 1}} T.{1,1}={0,1} In 3D: T= {{1, -1, 0}, {-1, 0, 1}, {1, 1, -1}} Tinverse = {{1, 1, 1}, {0, 1, 1}, {1, 2, 1}} T.{1,1,1}={0,0,1} In 4D: T= {{-1, -2, 0, 3}, {-2, -1, 0, 3}, {-1, 1, -1, 1}, {2, -2, 1, 0}}...

I have a vector of all ones in n-dimensions. For example (1,1,1) in 3D. I want to find a invertible rotation matrix T that transforms the vector of all ones to the vector (0,0,0,...,0,,1): Let v be the vector of all ones, and w=(0,0,...,0,1) Find T such that T.v == wIn low dimension it is easy...