Say, i have a vector a, defined in a coordinate system, x-y-z and i rotate the axes by an angle theta around the z-axis, so i have my z-component invariant in this change of basis. Can someone show me why,(adsbygoogle = window.adsbygoogle || []).push({});

[tex] a_x' = a_x cos\theta + a_y sin\theta [/tex] and

[tex] a_x' = -a_x sin\theta + a_y cos\theta [/tex]

i can't seem to find any place where they show how this is done.

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# Change of basis

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