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  • Least squares

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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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  1. 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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526–550 of 718 nodes
  • Orthogonality and projection#23893
  • Parametric form of the solution set of a system of linear equations#23419
  • Parametric vector form of the solution set of a system of linear equations#23420
  • Particular types of matrices#23535
  • Projection#23937
  • Proof of several equivalences for nonsingular matrix#23644
  • Pythagorean equality characterizes orthogonality over the reals#23918
  • QR decomposition#23630
  • Rank and nullity#23882
  • Rank and nullity#23672
  • Rank–nullity theorem for an m-by-n matrix#23679
  • Real block form and complex diagonalization for a 2-by-2 matrix#23618
  • Removing a linearly dependent vector from a set does not change the span of the set.#23982
  • R^n is a vector space.#24097
  • Row equivalence is an equivalence relation#23480
  • Row-equivalent augmented matrices represent equivalent systems#23769
  • Row equivalent matrices have the same row space.#23881
  • Row operations#23474
  • Row operations are given by multiplication by elementary matrices.#23559
  • Row operations do not necessarily preserve the column space.#23878
  • Scalar multiplication#23470
  • Scalar multiplication of matrices is associative and distributive#23473
  • Similarity of matrices#23634
  • Similarity of matrices is an equivalence relation#23636
  • Similar matrices have the same eigenvalues and the same characteristic polynomials.#23638
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  • Aspen Summer 2016 - Entanglement Matters#1213
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