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Hartley and Schaffalitzky, \cite{Hart-Schaf}, turns out to be a {\it generalized fundamental matrix}. Such matrices are studied in detail and, in particular, their rank is computed. The dimension of the variety that parametrizes such matrices is also determined. An algorithmic application of the generalized fundamental matrix to projective reconstruction is described. Response to Reviewers:page 4 -as requested, we have reminded the reader that the center of projection is a linear space of dimension k-h-1 page 15 -as requested, we have referenced the classical 7-point algorithm and added a reference to more recent analysis by Strumfels at al.

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Grassmann tensors arise from classical problems of scene reconstruction in computer vision. Trifocal Grassmann tensors, related to three projections from a projective space of dimension k onto view-spaces of varying dimensions are studied in this work. A canonical form for the combined projection matrices is obtained. When the centers of projections satisfy a natural generality assumption, such canonical form gives a closed formula for the rank of trifocal Grassmann tensors. The same approach is also applied to the case of two projections, confirming a previous result obtained with different methods in [6]. The rank of sequences of tensors converging to tensors associated with degenerate configurations of projection centers is also considered, giving concrete examples of a wide spectrum of phenomena that can happen. the quadrifocal tensor, respectively, and have been studied extensively, see for example [10], [1], [15], [2], [12]. In a more general setting, these tensors are called Grassmann tensors and were introduced by Hartley and Schaffalitzky, [11], as a way to encode information on corresponding subspaces in multiview geometry in higher dimensions. Three of the authors have studied critical loci for projective reconstruction from multiple views, [5], [8], and in this setting Grassmann tensors play a fundamental role, [7], [4].The authors' long-term goal is to study properties such as rank, decomposition, degenerations, and identifiability of Grassmann tensors in higher dimensions, and, when feasible, the varieties parameterizing such tensors.The first step was taken in [6], where three of the authors studied the case of two views in higher dimensions, introducing the concept of generalized fundamental matrices as 2-tensors. That first work contained an explicit geometric interpretation of the rational map associated to the generalized fundamental matrix, the computation of the rank of the generalized fundamental matrix with an explicit, closed formula, and the investigation of some properties of the variety of such objects.The next natural step in the authors' program is the study of trifocal Grassmann tensors, i.e. Grassmann tensors arising from three projections from higher dimensional projective spaces onto view-spaces of varying dimensions. A natural genericity assumption, see Assumption 5.1, allows for suitable changes of coordinates in the view spaces and in the ambient space that give rise to a canonical form for the combined projection matrices. Utilizing such canonical form, the rank of trifocal Grassmann tensors is computed with a closed formula, see Theorem 5.1. When Assumption 5.1 is no longer satisfied, the situation becomes quite intricate. A general canonical form for the combined projection matrices can still be obtained, see Section 6. We conclude with a series of examples in which the rank is computed utilizing the canonical form. These examples illustrate the wide spectrum of possible phenomena that can happen with the specialization of the three centers of projection. In particular, we p...

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