Let V, W be finite-dimensional inner product spaces and T € L(V, W). Prove: (a) If T is injective, then T"T is invertible and T† = (T*T)-'T". (b) If T is surjective, then TT* is invertible and T† =T"(TT*)-!.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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. Let V, W be finite-dimensional inner product spaces and T E L(V, W). Prove:
(a) If T is injective, then T*T is invertible and T† = (T*T)-!T*.
(b) If T is surjective, then TT* is invertible and T† =T*(TT*)-!.
1
Transcribed Image Text:. Let V, W be finite-dimensional inner product spaces and T E L(V, W). Prove: (a) If T is injective, then T*T is invertible and T† = (T*T)-!T*. (b) If T is surjective, then TT* is invertible and T† =T*(TT*)-!. 1
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