Research problem the matrix numerical range

Abstract
Every active mathematician has a storehouse of unresolved questions that he/she hopes someday to settle, but may never owing to changing interests, greener pastures elsewhere, or simply lack of a good idea. Since one mathematician's abandoned turf may be another's greener pasture, why not pose that unresolved question as a research problem? If it cannot be solved by anybody, the resulting publicity may confer luster on the proposer. and if it solved by somebody, the original proposer may be able to use the new ideas in further work. It's a winning stretegy to pose research problems, and a losing one not to since mathematics is a cooperative effort to reveal nature's truths

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