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Linear Algebra

Exercise 6.3.4

Answers

(b)

Compute

⟨ x, {(cT)}^{∗} (y) ⟩ = ⟨ cT (x), y ⟩ =

⟨ T (x), \bar{c} y ⟩ = ⟨ x, T^{∗} (\bar{c} y) ⟩ = ⟨ x, \bar{c} T^{∗} (y) ⟩

for all $x$ and $y$ .

(c)

Compute

⟨ x, {(TU)}^{∗} (y) ⟩ = ⟨ TU (x), y ⟩

= ⟨ U (x), T^{∗} (y) ⟩ = ⟨ x, U^{∗} T^{∗} (y) ⟩

for all $x$ and $y$ .

(e)

Compute

⟨ x, I^{∗} (y) ⟩ = ⟨ I (x), y ⟩

= ⟨ x, y ⟩ = ⟨ x, I (y) ⟩

for all $x$ and $y$ .

jephianlin

2011-06-27 00:00

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