In one of the exercises in the SVD section, we are asked to confirm that U, Vh are orthonormal. In Rachel’s answer, she mentioned that with the U matrix, we should do the multiplication testings with columns, so we are using
U.T @ U here. However with Vh we should be dealing with rows.
I am confused about this. Reading this post on Wolfram MathWorld, I think determining whether the matrices are orthonormal by doing
U.T @ U and
U @ U.T should yield the same result, and my experiment confirmed that. However, when I was trying to do
Vh.T @ Vh, the notebook immediately throws out a “MemoryError”. Running
Vh @ Vh.T was fine though. Why did this happen? Have I misunderstood something?
Thank you very much!