Abstract
Among the projectivities S of the ( m−1)-dimensional left-projective matrix space P m−1 ( M n ( C)), we characterize those which map the unit ball Δ onto itself. If the matrices S corresponding to S are of the form S=s T , where T is a J -unitary matrix and s ≠ 0 is an arbitrary complex number, then S maps Δ onto itself and keeps the hyperbolic distance invariant. Conversely, if the projectivity S maps Δ onto itself, then the corresponding matrices are of the above form. For the real scalar case P m−1 ( R) these results reduce to known facts of ordinary ( m−1)-dimensional projective geometry.
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