Linear Algebra/Projection

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Linear Algebra
 ← Changing Map Representations Projection Orthogonal Projection Onto a Line → 

This section is optional; only the last two sections of Chapter Five require this material.

We have described the projection  \pi from \mathbb{R}^3 into its  xy plane subspace as a "shadow map". This shows why, but it also shows that some shadows fall upward.

Linalg projection 1.png Linalg projection 2.png

So perhaps a better description is: the projection of \vec{v} is the \vec{p} in the plane with the property that someone standing on \vec{p} and looking straight up or down sees \vec{v}. In this section we will generalize this to other projections, both orthogonal (i.e., "straight up and down") and nonorthogonal.

Linear Algebra
 ← Changing Map Representations Projection Orthogonal Projection Onto a Line →