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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 projection of a vector which is in a subspace is the vector itself.

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The (orthogonal) projection of a vector onto a subspace is the point in the subspace closest to the vector.Close match
Definition of (orthogonal) projection onto a subspaceClose match
Formula for the coordinates of the projection of a vector onto a subspaceClose match
ProjectionClose match
Orthogonality and projectionClose match
Definition of (not necessarily orthogonal) projection onto a component of a direct sumClose match
The preimage of a vector is a translation of the kernel of the linear transformationClose 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
Formula for the (orthogonal) projection of one vector onto another vectorClose match
Definition of (orthogonal) projection of one vector onto another vectorClose match
The orthogonal complement of a subspace is a subspace.Close match
The direct sum of a subspace and its orthogonal complement is the whole space.Close match
Definition of a vector being orthogonal to a subspaceClose match
Subspaces associated to a linear transformationClose match
Example of a linear transformation on R^2: projectionClose match
The sum of subspaces is a subspaceClose match
Definition of subspaceClose match
A nonempty subset of a vector space is a subspace if and only if it is closed under linear combinationsClose match
The inverse image of a subspace under a linear transformation is a subspace.Related
A vector can be written uniquely as a linear combination of vectors from independent subspaces.Related

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