Say we have a transformation T[tex]\in[/tex]L(V). Now suppose a subspace of V (U) is in the rangespace of T. Now suppose P(adsbygoogle = window.adsbygoogle || []).push({}); _{U}v=u with u=a1u1+...+amvm.

Now apply T to u to get T(u)=b1u1+...+bmum=/=a1u1+...+amvm. What would happen

if we apply P_{U}to T(u)? In other words, what would we end up with after computing P_{U}T(u)?

I'm just wondering whether or not applying a transformation (a non-projection in this case) after a projection would result

in a different output after applying the projection to the image of T? In other words, would

P_{U}T(u) map to a1u1+..+amum or would it map to b1u1+..+bmum?

Thank you for your response!

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# Another question about projections.

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