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Orthogonality and projection

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Definition of (orthogonal) projection of one vector onto another vector
Formula for the (orthogonal) projection of one vector onto another vector
Definition of (not necessarily orthogonal) projection onto a component of a direct sum
Definition of (orthogonal) projection onto a subspace
The projection of a vector which is in a subspace is the vector itself.
The (orthogonal) projection of a vector onto a subspace is the point in the subspace closest to the vector.
Formula for the coordinates of the projection of a vector onto a subspace

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