Question
Asked Jan 24, 2020
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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*.

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Expert Answer

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

Algebra homework question answer, step 1, image 1

 

Algebra homework question answer, step 1, image 2
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Step 2

Now, It is given T is a linear operator on an inner product space V.  And

Algebra homework question answer, step 2, image 1

Suppose x and y are two vectors in the given inner space then we must have:

 

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Algebra homework question answer, step 2, image 2
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