- #1
indigojoker
- 246
- 0
I need to show:
[tex](\mathbf{\sigma} \cdot \mathbf{a})(\mathbf{\sigma} \cdot \mathbf{b})=\mathbf{a} \cdot \mathbf{b} I + i \mathbf{\sigma} \cdot (\mathbf{a} \times \mathbf{b})[/tex]
where a and b are arbitrary vectors, sigma is the pauli spin operator.
I was just wondering what the dot product and cross product were. Because a and b can be 2x1, 2x2, 2x3, etc... I'm not sure how to take a dot product of matricies much less a cross product. Since it specifies dot and cross, i assume that it is not just a regular matrix mulitpilication, however, i do not know how to take the dot and cross product of matrices. Any suggestions would be appreciated.
[tex](\mathbf{\sigma} \cdot \mathbf{a})(\mathbf{\sigma} \cdot \mathbf{b})=\mathbf{a} \cdot \mathbf{b} I + i \mathbf{\sigma} \cdot (\mathbf{a} \times \mathbf{b})[/tex]
where a and b are arbitrary vectors, sigma is the pauli spin operator.
I was just wondering what the dot product and cross product were. Because a and b can be 2x1, 2x2, 2x3, etc... I'm not sure how to take a dot product of matricies much less a cross product. Since it specifies dot and cross, i assume that it is not just a regular matrix mulitpilication, however, i do not know how to take the dot and cross product of matrices. Any suggestions would be appreciated.