for-v-y-x-v-R-2-v-has-basis-vectors-i-and-j-Assume-we-apply-a-basis-transform-to-obtain-new-basis-vectors-i-and-j-What-is-the-new-v-

Question Number 13942 by FilupS last updated on 25/May/17

for \boldsymbol v = [\begin{matrix} y \\ x \end{matrix}], \boldsymbol v \in R^{2}

\boldsymbol v has basis vectors \hat{i} and \hat{j}

Assume we apply a basis transform to

obtain new basis vectors {\hat{i}}^{'} and {\hat{j}}^{'}

What is the new \boldsymbol v^{'} ?

Answered by ajfour last updated on 25/May/17

\boldsymbol v^{'} = [\begin{matrix} y^{'} \\ x^{'} \end{matrix}] = [\begin{matrix} \hat{i} . {\hat{j}}^{'} & \hat{j} . {\hat{j}}^{'} \\ \hat{i} . {\hat{i}}^{'} & \hat{j} . {\hat{i}}^{'} \end{matrix}] [\begin{matrix} y \\ x \end{matrix}]

(m a y b e . .) .

Commented by FilupS last updated on 26/May/17

[\begin{matrix} \hat{i} . {\hat{j}}^{'} & \hat{j} . {\hat{j}}^{'} \\ \hat{i} . {\hat{i}}^{'} & \hat{j} . {\hat{i}}^{'} \end{matrix}] I have a feeling this is incorrect

I {don}^{'} t remember, but I think it should

be something like [\begin{matrix} \hat{i} & {\hat{i}}^{'} \\ \hat{j} & {\hat{j}}^{'} \end{matrix}]

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