Sign up ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Let {a1,a2,...,an} and {b1,b2,...,bn} be two bases for a vector space E. Fix p, 1 ≤ p ≤n. Is there a permutation σ such that {a1,a2,...,ap,bσ(p+1),...,bσ(n)} and {bσ(1),bσ(2),...,,bσ(p),ap+1,...,an} are both bases of E?

This question is the last exercise of the first chapter in the book Linear Algebra by Greub. I can prove the case p=n-1.

share|cite|improve this question
COuld you explain why such a fact is interesting/useful? – Mariano Suárez-Alvarez Jan 8 '10 at 1:31
No. I´ve no idea why anyone would care about it. It´s just an exercise in a book of linear algebra. – Julio Cesar da Silva Jan 8 '10 at 14:59

1 Answer 1

up vote 4 down vote accepted

It's also Theorem 7.2 in Prasolov's Problems in Linear Algebra, which gives a proof and attributes it to Green 1973.

share|cite|improve this answer
Included link is broken. – Turbo Apr 10 at 5:06

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.