Around 4:20 (!) you say that those 3 matrices J1, J2, and J3 are a basis for any real 3x3 skew-symmetric matrix. But all 3 of those matrices have all zeros along the diagonal. So, how can any linear combination of J1, J2, J3 ever add up to be a skew-symmetric matrix with non-zero values along the diagonal? (you said earlier that such matrices exist, just with the restriction that the diagonal numbers have to add to zero)
@acephysics123
24 күн бұрын
You are absolutely correct. Skew Symmetric matrices are defined such that A transpose =-A and therefore, the diagonal elements must be zero. Thank you for your comment, clarification, and correction.
@miro.s
18 күн бұрын
What you described is happening with Hermitian matrices. Antihermitian as skew symmetric has zeros on diagonal.
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