Matrix tuples with invariant subspaces of dimensions summing to the space dimension but not spanning it form an algebraic hypersurface whose equation is explicitly derived.
Frenkel:The triangulant,Linear Algebra and its Applications 709 (2025), 92–110
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Matrix tuples with linearly dependent invariant subspaces
Matrix tuples with invariant subspaces of dimensions summing to the space dimension but not spanning it form an algebraic hypersurface whose equation is explicitly derived.