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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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The (orthogonal) projection of a vector onto a subspace is the point in the subspace closest to the vector.

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Definition of (orthogonal) projection onto a subspaceClose match
Orthogonality and projectionClose match
The projection of a vector which is in a subspace is the vector itself.Close match
Formula for the coordinates of the projection of a vector onto a subspaceClose match
Definition of (not necessarily orthogonal) projection onto a component of a direct sumClose match
A vector can be written uniquely as a sum of a vector in a subspace and a vector orthogonal to the subspace.Close match
Definition of (orthogonal) projection of one vector onto another vectorClose match
The orthogonal complement of a subspace is a subspace.Close match
Formula for the (orthogonal) projection of one vector onto another vectorClose match
The direct sum of a subspace and its orthogonal complement is the whole space.Close match
Definition of orthogonal complement of a subspaceClose match
Definition of a vector being orthogonal to a subspaceClose match
ProjectionClose match
A vector is in the orthogonal complement of a subspace if and only if it is orthogonal to every vector in a basis of the subspace.Close match
Definition of orthogonal subspacesClose match
OrthogonalityClose match
Definition of orthogonal basis of a (sub)spaceClose match
Example of a linear transformation on R^2: projectionRelated
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