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Orthogonality and projection

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Definition of least-squares solution to a linear system
Definition of least-squares error of a linear system
Formula for computing the least squares solution to a linear system.
Formula for computing the least squares solution to a linear system
The least squares solution to a linear system is unique if and only if the columns of the coefficient matrix are linearly independent.
Definition of the least-squares linear fit to 2-dimensional data
Formula for the least-squares linear fit to 2-dimensional data

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Definition of least-squares error of a linear systemClose match
Definition of least-squares solution to a linear systemClose match
The least squares solution to a linear system is unique if and only if the columns of the coefficient matrix are linearly independent.Close match
Formula for computing the least squares solution to a linear system.Close match
Definition of the least-squares linear fit to 2-dimensional dataClose match
Orthogonality and projectionClose match
Formula for computing the least squares solution to a linear systemClose match
Formula for the least-squares linear fit to 2-dimensional dataClose match
The matrix equation Ax=b has a solution if and only if b is a linear combination of the columns of A.Related
Equivalence theorem for nonsingular matrices: the equation Ax=b has a unique solution for all b.Related
Equivalence theorem for nonsingular matrices: the equation Ax=b has a solution for all b.Related
The (orthogonal) projection of a vector onto a subspace is the point in the subspace closest to the vector.Related
Formula for the (orthogonal) projection of one vector onto another vectorRelated
OrthogonalityRelated
The Gram-Schmidt process converts a linearly independent set into an orthogonal set.Related
ProjectionRelated
A matrix with real entries and orthonormal columns preserves norms.Related
Formula for the coordinates of the projection of a vector onto a subspaceRelated
Definition of Gram-Schmidt processRelated
Norm and lengthRelated

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