Wednesday, 23 December 2015

matrices - Change of basis matrix verification

Let B and C be two bases. To find the change of basis matrix ϕB,C, I compute ϕSB,B and ϕSB,C. Create the new matrix T=[ϕSB,B|ϕSB,C]. Reducing it to reduced row echelon form, should yield T=[I|ϕB,C, right? Is there a way to verify that the new basis indeed maps [v]B to [v]C?

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