A projection is a function that fixes the points in its image: applying it twice has the same effect as applying it once. A coordinate projection can be represented this way when its target is identified with a retract; a linear projection additionally respects the vector-space operations.
For a coordinate projection map onto , write for the other factor. The map is surjective exactly when is empty or is nonempty. It is injective exactly when is empty or has at most one element. In particular, a surjection onto an empty Cartesian product need not induce a surjection onto a nonempty factor.
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In mathematics, "projection" can refer to several concepts depending on the context, but it typically involves the idea of reducing a higher-dimensional object to a lower-dimensional representation or mapping points from one space to another. Here are some common interpretations of projection: 1. **Linear Projection in Linear Algebra**: In the context of vector spaces, a projection refers to a linear transformation that maps a vector onto a subspace.
