Re:Robotics 501: Mathematics for Robotics
by enriquto on Thursday January 27, 2022 @12:35PM
(#30103438)
> What is the point of explaining, say the QR factorization (...) engineers?
As a personal data point, I'm a mathematician that regularly teaches the QR and SVD factorizations to engineers. Not because I find them interesting, but because they need it for their daily jobs and they ask me to.
More precisely, they are engineers working in the geometrical modelling of satellite sensors, doing "computer vision" from satellite images. The QR and SVD factorizations of 3 and 4-dimensional matrices are essential tools for the bundle adjustment steps, to represent the position and orientation of each satellite and the transformations between them. A crucial idea (for them) is that A=QR is a unique decomposition of A which is also continuous (the coefficients of Q and R depend smoothly on the coefficients of A). On the contrary, the SVD decomposition is neither unique nor continuous. Since the SVD provides an easier-to-use decomposition, you want to use it whenever possible, but being careful to never assume continuity nor uniqueness; if you need these properties then you pick the QR.
As a personal data point, I'm a mathematician that regularly teaches the QR and SVD factorizations to engineers. Not because I find them interesting, but because they need it for their daily jobs and they ask me to.
More precisely, they are engineers working in the geometrical modelling of satellite sensors, doing "computer vision" from satellite images. The QR and SVD factorizations of 3 and 4-dimensional matrices are essential tools for the bundle adjustment steps, to represent the position and orientation of each satellite and the transformations between them. A crucial idea (for them) is that A=QR is a unique decomposition of A which is also continuous (the coefficients of Q and R depend smoothly on the coefficients of A). On the contrary, the SVD decomposition is neither unique nor continuous. Since the SVD provides an easier-to-use decomposition, you want to use it whenever possible, but being careful to never assume continuity nor uniqueness; if you need these properties then you pick the QR.