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Social ScienceLet T be a linear operator on an inner product space V. Let U1= T + T* and U2 = TT*. Prove that U1 = U1* and U2= U2*.
Let T be a linear operator on an inner product space V. Let U1= T + T* and U2 = TT*. Prove that U1 = U1* and U2= U2*.
Expert Answer
If T is an operator in an inner product space V over the field F together with an inner product, i.e., with a map
Now, It is given T is a linear operator on an inner product space V. And
Suppose x and y are two vectors in the given inner space then we must have:
...
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