Question

(i) Let V be a finite-dimensional inner product space, and let B be an orthonormal basis of V. Show that ?v, w? = [v]B · [w]B for all v, w ? V. (ii) Let V be a finite-dimensional vector space, and let B be a basis of V. Show that there is an inner product on V for which B is orthonormal.

          (i) Let V be a finite-dimensional inner product space, and let B be an orthonormal basis of V. Show that
?v, w? = [v]B · [w]B
for all v, w ? V.
(ii) Let V be a finite-dimensional vector space, and let B be a basis of V. Show that there is an inner product on V for which B is orthonormal.

(i) Let V be a finite-dimensional inner product space, and let B be an orthonormal basis of V. Show that
?v, w? = [v]B · [w]B
for all v, w ? V.
(ii) Let V be a finite-dimensional vector space, and let B be a basis of V. Show that there is an inner product on V for which B is orthonormal.

Added by Melissa B.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert Sri K

09/30/2022

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(i) Let V be a finite-dimensional inner product space, and let B be an orthonormal basis of V. Show that ✨v, w✩ = [v]B · [w]B for all v, w ∈ V. (ii) Let V be a finite-dimensional vector space, and let B be a basis of V. Show that there is an inner product on V for which B is orthonormal.