Linear algebra is the mathematics of phenomena that depend linearly on several parameters. Such phenomena can be modeled by systems of linear equations. We will discuss algorithms for computing solutions to systems of linear equations using matrices, rectangular arrays of numbers. Matrices can also be viewed geometrically as linear transformations on n-dimensional space. This viewpoint provides a segue to the notion of a linear transformation of an abstract vector space. We use eigenvectors and eigenvalues to describe the action of matrices and linear transformations in terms of simpler scaling actions. Finally we discuss a generalization of the dot product, the inner product, which encodes all the geometric information (length, distance, orthogonality) about a vector space, and, in particular, provides a notion of approximation in vector spaces.
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