Geodesic
Converting column majorization
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXIII, Tome 496 (2020), pp. 195-215

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The paper characterizes linear operators converting column majorization into weak, directional, and strong majorizations. An example of a linear converter from weak, directional, and strong majorizations to column majorization preserving none of these majorizations is provided. 
@article{ZNSL_2020_496_a14,
     author = {P. M. Shteyner},
     title = {Converting column majorization},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {195--215},
     publisher = {mathdoc},
     volume = {496},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_496_a14/}
}
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P. M. Shteyner. Converting column majorization. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXIII, Tome 496 (2020), pp. 195-215. http://geodesic.mathdoc.fr/item/ZNSL_2020_496_a14/