Question
Let V be a finite dimensional vector space and consider S,T in End(V). 1. Show that ST is invertible if and only if both S
Let V be a finite dimensional vector space and consider S,T in End(V).
1. Show that ST is invertible if and only if both S and T are invertible.
2. Prove that ST=I iff TS=I
3. Give an example illustrating that both 1 & 2 are false over an infinite dimensional vector space.
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An Introduction to the Mathematics of Financial Derivatives
Authors: Ali Hirsa, Salih N. Neftci
3rd edition
012384682X, 978-0123846822
