. 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

Injective Function: A function is said to be injective if each element of the codomain is mapped to…

Answered: Let V, W be finite-dimensional inner…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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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*)-!.

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† = (TT)-'T". (b) If T is surjective, then TT is invertible and T† =T"(TT*)-!.