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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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The least squares solution to a linear system is unique if and only if the columns of the coefficient matrix are linearly independent.

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Least squaresClose match
Definition of least-squares solution to a linear systemClose match
A set of vectors is linearly independent if and only if the homogeneous linear system corresponding to the matrix of column vectors has only the trivial solution.Close match
Definition of least-squares error of a linear systemClose match
Eigenvectors with distinct eigenvalues are linearly independent.Close match
Equivalence theorem for nonsingular matrices: the columns of A are linearly independent.Close match
Description of a basis for the null space of a matrix from the reduced row-echelon form.Close match
Formula for computing the least squares solution to a linear system.Close match
A set of vectors is linearly independent if and only if the matrix of column vectors in reduced row-echelon form has every column as a pivot column.Close match
Definition of trivial solution to a homogeneous linear system of equationsClose match
If a set of vectors contains the 0 vectorClose match
A linear system is equivalent to a vector equation.Close match
Definition of the least-squares linear fit to 2-dimensional dataClose match
Theorem: a set of vectors is linearly independent if and only if whenever a linear combination is 0Close match
An orthogonal set of nonzero vectors is linearly independent.Related
A set is linearly independent if and only if the set of coordinate vectors with respect to any basis is linearly independent.Related
The minimal polynomial of a square matrix exists and is unique.Related
The nonzero rows of an echelon form of a matrix are linearly independent.Related
Definition of linearly independent set of vectors: if a linear combination is 0Related
Formula for computing the least squares solution to a linear systemRelated

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