Some practical applications of SVD
I noticed a thread on LinkedIn on practical applications of SVD. I had to add my 2 cents given how much I have used SVD to solve practical problems.
SVD Decomposition
where \(A∈R^{mxn}\)
SVD is both a mathematical and a computational tool. Some applications from the top of my head:
With full SVD, the entries of the U, V matrix contains the basis for the 4 fundamental subspaces.
An extremely important tool in estimation. Helps identify and fix ill-conditioned matrices when estimating 'x' in y = Ax.
SVD is used to compute pseudo inverse when
A is square and non-invertible.
A is skinny but not full-column rank.
A is fat and not a full-row rank
SVD is used in optimization to compute max/min values of a quadratic cost fn subject to unit norm constraints.
In robotics, to handle singularities.
Understanding which directions in the state space require the least control effort. Also, directions can be estimated easier than others.
I can go on and on. It's one of the most powerful computational tools if u know when and how to use it. Unfortunately, most YouTube videos barely scratch the surface and mostly talk about visual intuition which IMO is the least important aspect of SVD.
Click here for the LinkedIn Thread
PS: The post assumes that you have a basic familiarity with SVD and talks only about applications. If you want to discuss the basics of SVD, leave a comment. Happy to also go into detail on each of the applications mentioned above.