I am currently reading a book on data analysis (Nathan Kutz, Data-Driven Modeling & Scientific Computation) and a bit stuck in the chapter about SVD.
It states that SVDs can be used to handle rank deficient matrices, but I do not understood why that actually is true. The book explains that "silent" columns are added to the Û matrix, these are orthonormal to the existing set in Û. Also, "silent" rows of all zero elements are added to the E matrix. This procedure would make it obvious that SVD can handle rank deficient matrices, the following illustration is provided:
(copied from p. 379 of the book). Would someone be so kind and explain why these two steps are necessary to let SVD handle rank deficient matrices? Thank you!