Multi-Way Decomposition for Oblique Projection and Its Applications
Xuejing Zhang
Abstract
Xuejing Zhang
Abstract
In this paper, the oblique projection is revisited by presenting some new findings. It is proved that an orthogonal projector can be expressed as a summation of multiple oblique projectors, each of which has a specific range and null space. Several geometrical illustrations are presented to provide a better understanding of the proposed model. Some applications of the multi-way decomposition of oblique projection are demonstrated.
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In this paper, the oblique projection is revisited by presenting some new findings. It is proved that an orthogonal projector can be expressed as a summation of multiple oblique projectors, each of which has a specific range and null space. Several geometrical illustrations are presented to provide a better understanding of the proposed model. Some applications of the multi-way decomposition of oblique projection are demonstrated.
Key concepts: Oblique projection, Oblique case, Projection (relational algebra), Decomposition, Projector, Computer science, Orthographic projection, Null (SQL)