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\section*{Unit 2:  Least squares and determinants}

Each component of a vector in $\R^n$ indicates a distance along one of the coordinate axes.  This practice of dissecting a vector into directional components is an important one.  In particular, it leads to the ``least squares'' method of fitting curves to collections of data.
This unit also introduces matrix {\em eigenvalues} and {\em eigenvectors}. 
Many calculations become simpler when working with a basis of eigenvectors.

The {\em determinant} of a matrix is a number characterizing
that matrix.  This value is useful for determining whether a matrix is
singular, computing its inverse, and more.

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