# How to write a matrix in a different basis?

Posted 11 days ago
169 Views
|
5 Replies
|
2 Total Likes
|
 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
Sort By:
Posted 11 days ago
 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:
Posted 11 days ago
 I cannot understand what is going on there. It works on my system. Did you copy/paste or did you type the commands?