Let $V$ be a vector space of dimension $n$. It is well known that when $r | n$, there is a set of disjoint $r$-dimensional subspaces of $V$, which covers $V$, called Spread. My question is that is a $r$- dimensional spread in $V$ unique?
2026-03-28 16:04:00.1774713840
Is a Spread Unique?
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It is not unique (even up to isomorphism), at least over finite fields. Several examples are known, but the constructions are hard. The classical construction is called the Desarguesian spread. If you google for "non-Desarguesian spread" you will find articles where other constructions are explained.
(Most articles study this in the projective setting, but they are easily convertible.)