Tuesday, October 30, 2007

Linear Independence

This problem is the generalization of exercise 2.3.9 from 'linear algebra' Hoffman and Kunze.

Let the set of vectors be linearly independent. Prove that are also linearly independent given

I mean

and so on.

ps: I proved it by proving a certain matrix to be invertible and that was pretty cumbersome. Hoping for a better pretty solution :)

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