Given a 2×3 matrix, the Singular Value Decomposition would give the matrix U which would be a 2x2 matrix and VT (transpose of V), a 3x3 matrix. From what I understand, the matrices U and V describe the amount of rotation the matrix A would induce to any vector x. So, my question is, how can I find the angle of rotation using U and V. Are they different angles, or a single angle computed as some combination of U and V.
I am fairly new to this, so any direction is much appreciated.
2026-03-27 12:27:31.1774614451
SVD - Finding the angle of rotation from U and V
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In general, they are different angles. You can get the angle of the 2x2 by taking the arcsin of the lower left element. You can get the angle of the 3x3 by using the method here.