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Totally Nonnegative Matrices by Charles R. Johnson, Shaun M. Fallat

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Chapter Two

Bidiagonal Factorization

2.0 INTRODUCTION

Factorization of matrices is one of the most important topics in matrix theory, and plays a central role in many related applied areas such as numerical analysis and statistics. In fact, a typical (and useful) preliminary topic for any course in linear algebra is Gaussian elimination and elementary row operations, which essentially represents the groundwork for many forms of matrix factorization. In particular, triangular factorizations are a byproduct of many sorts of elimination strategies including Gaussian elimination.

Investigating when a class of matrices (such as positive definite or ...

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