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V and W are finite dimensional inner product spaces,T: V?W is a linear map 1A: Give an...

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Advance Math

V and W are finite dimensional inner product spaces,T: V?W is alinear map

1A: Give an example of a map T from R2 to itself (with the usualinner product) such that?Tv,v?= 0 for every map.

1B: Suppose that V is a complex space. Showthat?Tu,w?=(1/4)(?T(u+w),u+w???T(u?w),u?w?)+(1/4)i(?T(u+iw),u+iw???T(u?iw),u?iw?

1C: Suppose T is a linear operator on a complex space suchthat?Tv,v?= 0 for all v. Show that T= 0 (i.e. that Tv=0 for allv).

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