Abstract Linear Algebra I
Least squares approximation is a mathematical method used to find the best-fitting line or curve for a set of data points by minimizing the sum of the squares of the differences between the observed values and the values predicted by the model. This technique relies on inner product spaces to determine distances, utilizes orthogonal projections to compute the closest approximation in a linear sense, and can be enhanced using processes like Gram-Schmidt for orthonormal bases, ultimately facilitating efficient QR decomposition for solving systems of equations.
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