Mordred
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Mordred, I have a technical question here.... my work is a bit more complicated and requires a bit more depth than I am used to - in the case of a projective space, the identity P^2 = P is said to hold - what does it mean?
In my case I am looking at, I have an antisymmetric matrix that requires to be squared in the projected space to yield the identity/unity. The projective space looks like
[math]P = \frac{\mathbf{I} + n \cdot \sigma}{2} = |\psi><\psi|[/math]The square of the Pauli matrix should yield an identity [math](n \cdot \sigma)^2 = \mathbf{I}[/math] (unit vectors naturally square into unity). What is the square of the dyad in such a case?
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I have a feeling this isn't the case though, as it is possible say [math]\mathbf{I} = \sum_j |j><j|[\math] where we take [math]<j|k> = \delta_{ij}[/math], so just a bit confused about the dyad.
that should be [math]\mathbf{I} = \sum_j\ <j|j>\ = \delta_{ij}[/math]
with [math]\delta_{ij} =\ <i|j>[/math] sorry. Tired and heading to bed soon.
It's probably true what I have said, not sure why I thought it needs to square to unity. It seems n|\sigma> = 1 (is this always the case) anyway, good night.
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