I am familiar with singular value decomposition based definition of separable matrix which counts on the number of non-zero singular values. If there is only one non-zero $\sigma$, matrix is rank-1/separable matrix else it is termed as non-separable. However a quick google search reveals terms like
- Disjunct matrix/d-separable matrix
followed by
- Almost Separable Matrix https://arxiv.org/abs/1410.1826
- Piecewise Separable Matrix http://www.inm.ras.ru/library/Tyrtyshnikov/biblio/separ-calcolo.pdf
- Strongly Separable Matrix http://www.ntu.edu.sg/home/hjwei/cjc65/Slides/Jul-16-SR-Miao.pdf
I have not seen these terms showing up in SVD related definition. Could someone please elaborate on the connection , if any, between these and svd based rank-1 definition of separable matrix.