Transcription of FACTORIZATION of MATRICES - University of Texas at Austin
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FACTORIZATION of MATRICES - University of Texas at Austin
FACTORIZATION of MATRICES Let's begin by looking at various decompositions of MATRICES , see also Matrix FACTORIZATION . In CS, thesedecompositions are used to implement efficient matrix algorithms. Indeed, as Lay says in his book: "In the language of computer science, the expression of as a product amounts to a pre-processing ofthe data in , organizing that data into two or more parts whose structures are more useful in some way,perhaps more accessible for computation."Nonetheless, the origin of these factorizations lies long in the past when they were first introduced by variousmathematicians after whom they are frequently named (though not always, and not always chronologicallyaccurately, either!). Their importance in math, science, engineering and economics quite generally cannot beover-stated, however. As Strang in his book says: "many key ideas of linear algebra, when you look at them closely, are really factorizations of a original matrix becomes the product of 2 or 3 special MATRICES .
method of elimination for solving systems of linear equation. A A A ... elementary matrices, is lower triangular with entries on the diagonal and is upper triangular. Fundamental Theorem 2 is the version that's most often used in large scale computations. But rather than
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