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13.
Moving zeros among matrices. Appendix, Upper-forms for pairs of matrices
Holbrook, John ...
V delu raziskujemo vzorce ničelnih elementov v eni ali več matrikah, ki jih lahko dosežemo s hkratno unitarno podobnostjo. Dokažemo posplošitev Patijeva izreka o tridiagonalizaciji poljubne ▫$4 ...\times 4$▫ matrike na pare takih matrik. Tak par s hkratno unitarno podobnostjo prevedoma na par matrik v Hessenbegovi formi. Naše delo se bistveno naslanja na poenastavljen dokaz Patijevaga izreka, ki sta ga objavila Davidson in Djoković. Prednost pristopa prek Hessenbegove forme je v tem, da lahko uporabimo podobnost s poljubno obrnljivo matriko. Tako dokažemo posplošitev nad poljubnim algebraično zaprtim obsegom. Dokažemo tudi analogen izrek za ▫$5 \times 5$▫ in večje matrike.
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