Below I examine the effect of elementary symmetric matrices on a projective base and find the kind of the projective map it defines.

All points of the x=0 line (yB+zC) remain fixed. Also point A is fixed under the map F, which is a

Analogous interpretation in the case k takes the place of an other diagonal entry.

All points of the line z=0 remain fixed. All lines through the point O=aA+bB remain invariant.

Hence the map is in this case an

P

All points of the line y=0 remain fixed. All lines through the point C remain invariant. Hence the map is in this case also an

A projectivity of period 2, hence a

Analogous to the previous, the other permutations of rows give

In the file Elation.html I discuss the decomposition of an elation in a product of two harmonic homologies.

ProjectivityResolutionPerspectivities.html

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