Exercise 7.D.7

Answers

Proof. A quick calculation, like the ones in the previous exercises, shows that

T∗T(z 1,z2,z3) = (4z1,9z2,z3).

Thus

T∗T(z1,z2,z3) = (2z1,3z2,z3).

Define S ∈L(𝔽3) by

S(z1,z2,z3) = (z3,z1,z2).

S is clearly an isometry (it maps the standard basis, which is orthonormal, to a permutation of the standard basis) and we have ST∗ T = T. □

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2017-10-06 00:00
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