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How to write a matrix in a different basis?

Posted 11 days ago
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Hi!

I have these two 4x4 matrix

Subscript[S, 1] = KroneckerProduct[PauliMatrix[1], IdentityMatrix[2]]

Subscript[S, 2] = KroneckerProduct[IdentityMatrix[2], PauliMatrix[2]]

Which are written in the Canonical basis ({{1}, {0}, {0}, {0}}; {{0}, {1}, {0}, {0}}; {{0}, {0}, {1}, {0}}; {{0}, {0}, {0}, {1}})

I would like to write down these two matrices in the following basis:

G := {{0}, {0}, {0}, {1}}

S := (1/Sqrt[2]) {{0}, {1}, {1}, {0}}

A := (1/Sqrt[2]) {{0}, {1}, {-1}, {0}}

E := {{1}, {0}, {0}, {0}}

Is there any way to do it in Mathematica?

Thanks in advance

5 Replies

According to my books this should be done by

m1 = KroneckerProduct[PauliMatrix[1], IdentityMatrix[2]];
mT = {
   {0, 0, 0, 1},
   {0, 1/Sqrt[2], 1/Sqrt[2], 0},
   {0, 1/Sqrt[2], -1/Sqrt[2], 0},
   {1, 0, 0, 0}};


m1T = Inverse[mT].m1.mT;
m1T // MatrixForm
Posted 11 days ago

Thanks for the answer!

I understood what you have done but when I reply it I do not get a matrix as the result. Instead, I get the following result: My result

I cannot understand what is going on there. It works on my system. Did you copy/paste or did you type the commands?

Posted 11 days ago

Sorry! The problem was my code. It works here now. Thank you very much!

Posted 10 days ago

Crossposted here.

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