Mathematics, 02.06.2020 05:59 lexipeacemaker
Assume {v1, . . . , vn} is a basis of a vector space V , and T : V > W is an isomorphism where W is another vector space. Show that the vectors w1 = T(v1), . . . ,wn = T(vn) are a basis of W.
This statement becomes false if we drop the assumption that T is invertible. Demonstrate this by finding a counterexample.
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