Let B={(adsbygoogle = window.adsbygoogle || []).push({}); b} and C={_{1},b_{2}c} be basis. Then the change of coordinate matrix P(C to B) involves the C-coordinate vectors of_{1},c_{2}b_{1}andb_{2}. Let

[b1]c=[x1] and [b2]c=[y1]

.........[x2]................[y2].

Then by definition [c1 c2][x1]=b1 and [c1 c2][y1]=b_{2}. I dont get how you can

................................. [x2].....................[y2]

multiply the matrix with basis set C with the change of coordinate matrix P(C to B) to get back basis set B ?

Can anyone help me understand how the derive the fact that you can take the set C basis and matrix P to get basis b1 and b2? My textbook just says very little about it.

Here is an example of a problem relating to this idea.

There was a problem that stated find a basis {u} for R^3 such that P is the change of coordinates matrix from{_{1},u_{2},u_{3}u} to the basis {_{1},u_{2},u_{3}v}? P was given and_{1},v_{2},v_{3}vwere given as well. I know how to do it but don't get the how it works?_{1},v_{2},v_{3}

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# Change of basis theorem?

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