Matrix Transformations and Factorizations
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In most applications of linear algebra, problems are solved by transformations of matrices. A given matrix (which represents some transformation of a vector) is itself transformed. The simplest example of this is in solving the linear system Ax = b, where the matrix A represents a transformation of the vector x to the vector b. The matrix A is transformed through a succession of linear operations until x is determined easily by the transformed A and the transformed b.
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