Linear algebra and statistics
Abstract
Important mathematical concepts in linear algebra, including the inner product, linear mapping, and the adjoint of a linear mapping, are reviewed. Reviewed first is the linear least-squares fitting technique. It provides an estimate of a set of unknown variables in an overdetermined system or model where the total number of unknowns is larger than the total number of equations for a given set of data. Important components in data fitting that are discussed are the data, the model, the error distribution, a statistical method of estimate, and the dependence of errors in the estimate to errors in the data. It is shown that a seemingly deterministic least-squares fit is the result of a statistical estimate ...
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