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Exercise 6.A.23

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Proof. We have $⟨ (v_{1}, \dots, v_{m}), (v_{1}, \dots, v_{m}) ⟩ = ⟨ v_{1}, v_{1} ⟩ + \dots + ⟨ v_{m}, v_{m} ⟩$ . Positivity and definiteness follow directly from the fact that $⟨ v_{j}, v_{j} ⟩ \geq 0$ for each $j$ . The remaining properties follow easily from the definitions. □

celiopassos

2017-10-06 00:00

Exercise 6.A.23

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