Matrix formulation of an operator

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The discussion revolves around the difficulties in applying the operator R to the basis vectors |bj> in an N-dimensional linear vector space. The user successfully derived the matrix representation of R but is confused as it does not yield the expected results, specifically that R|bj> should equal |b(j+1)>. Instead, they observe incorrect behavior resembling R|bj> = |b(j-1)>. Participants suggest verifying the matrix multiplication process and clarify the correct representation of basis vectors, emphasizing the importance of mastering matrix operations. The user acknowledges errors in their understanding of the matrix and basis vectors, indicating a need for further clarification on these concepts.
  • #31
tanaygupta2000 said:
Sir please assist me where am I doing mistake.View attachment 278400
That's simply wrong. I can't imagine what process you're using for matrix multiplication of a vector, but it's not the right one.
 
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  • #32
tanaygupta2000 said:
I just tried using a hermitian of R since it is behaving like a rotation matrix and I got ... is this good?View attachment 278403
You're matrix multiplication is correct, but you have the wrong idea about what a basis vector is.
 
  • #33
PeroK said:
You're matrix multiplication is correct, but you have the wrong idea about what a basis vector is.
You told it is b1> = transpose(1, 0, 0, ...,)
 
  • #34
tanaygupta2000 said:
You told it is b1> = transpose(1, 0, 0, ...,)
Which is right. You're confusing it with the first component of a vector.
 
  • #35
PS The root of your problem is that you haven't mastered matrices and vectors. You have basic errors and confusions.
 

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