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)
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.
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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)
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.
What you described is happening with Hermitian matrices. Antihermitian as skew symmetric has zeros on diagonal.
@@miro.s yes thank you!
This is amazing timing!
Cool! Why is it amazing timing??
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