Unformatted text preview: of just linear operators) as given in the deﬁnition on page 367. Please answer the following questions regarding adjoints of linear transformations. Let T : V → W be a linear transformation, where V and W are ﬁnite-dimensional inner product spaces with inner products h· , ·i 1 and h· , ·i 2 , respectively. (a) Prove that [ T * ] β γ = ([ T ] γ β ) * , where β and γ are orthonormal bases for V and W , respectively. (b) Prove that that the null space of T is equal to the orthogonal subspace of the range space of T * , i.e., ( R ( T * )) ⊥ = N ( T ). 6. (24%) Problem 7 of Section 6.4 7. (6%+6%) Problem 17 (a), (b) of Section 6.4. 8. (10%) Problem 10 of Section 6.5 9. (20%) Problem 29 of Section 6.5. 1...
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- Spring '11
- Linear Algebra, TA, Inner product space, Prove Theorem