we choose a basis B={v1=(1,0)v2=(1,1)} from and define why does the prof say that how did he get those formulas? and i cant se the structure of our chosen basis here? how to see it in thos formulas ?
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Originally Posted by transgalactic we choose a basis B={v1=(1,0)v2=(1,1)} from and define why does the prof say that Although I don't know what is the final question, taking into account that is a basis of , every can be uniquely expressed in the way . Same considerations for .
if x=(x1,x2) then x could be represented as only if v1=(1,0) v2=(0,1) but here we have a different basis not a standart one. so our coefficient is not x1 x2 ??
Perhaps this simple example will help you. Consider and . Prove that and . According to the given definition of the inner product we have .
ok so if i will go by your example (x,y)_B=x1y1+x2y2=5*2+2*1=12 x=(5,2)=5(1,0)+2(1,1)=(7,2) i try to follow the logic but i cant understand this term
Originally Posted by transgalactic x=(5,2)=5(1,0)+2(1,1)=(7,2)
i know i got here some thing wrong just cant understand this basis of inner product i am looking for a tutorial with basic examples
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