## Classification of canonical bases for $$(n-1)$$-dimensional subspaces of $$n$$-dimensional vector space.(English)Zbl 1392.15003

Summary: Canonical bases for $$(n-1)$$-dimensional subspaces of $$n$$-dimensional vector space are introduced and classified in the article. The result is very prospective to utilize canonical bases at all applications. For example, maximal subalgebras of Lie algebras can be found using them.

### MSC:

 15A03 Vector spaces, linear dependence, rank, lineability 17B05 Structure theory for Lie algebras and superalgebras
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