Question

Asked Jan 24, 2020

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Let T be a linear operator on an inner product space V. Let U_{1}= T + T* and U_{2} = TT*. Prove that U_{1} = U_{1}* and U_{2}= U_{2}*.

Step 1

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

Step 2

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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