3. Let TUV and S: V→ W. We have that SoT: U → W. Prove that (SoT)* = T* o S*. 4. Let v₁,.., Un EV be a basis of V. (a) Define the dual basis vi,.., v € V*. (b) Prove that formula: a = Ei=1:na (vi) v for every a € V*. (c) Prove the reciprocal formula: v = Ei=1:n v; (v) v₁ for every v € V.

3. Let TUV and S: V→ W. We have that SoT: U → W. Prove that (SoT)* = T* o S. 4. Let v₁,.., Un EV be a basis of V. (a) Define the dual basis vi,.., v € V. (b) Prove that formula: a = Ei=1:na (vi) v for every a € V*. (c) Prove the reciprocal formula: v = Ei=1:n v; (v) v₁ for every v € V.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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