For any vector in Rn and any permutation of the numbers 1, 2, , n (that is, is a rearrangement of those numbers into a new order), define () to be the vector whose components are v(1), v(2), , and v(n) (where (1) is the first number in the rearrangement, etc ) Now fix and let V be the span of () pe...

The possibilities for the dimension of V are 0 1 n 1 and n To see this first consider the case ...

For any vector in Rn and any permutation of the numbers 1, 2, . .

Question:

For any vector in Rn and any permutation σ of the numbers 1, 2, . . . , n (that is, σ is a rearrangement of those numbers into a new order), define σ() to be the vector whose components are vσ(1), vσ(2), . . . , and vσ(n) (where σ(1) is the first number in the rearrangement, etc.). Now fix and let V be the span of {σ()} σ permutes 1, . . . , n}. What are the possibilities for the dimension of V?