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

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Chapter Nine

Extensions and Completions

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The property that a matrix be TP is sufficiently strong that, at first glance, construction seems even more difficult than recognition. Of course, the elementary bidiagonal factorization provides an easy way simply to write down an example, but with this factorization it is very difficult to “design” many entries of the resulting matrix. Here, we review a variety of construction, extension and completion ideas for both TP and TN matrices.

Another way to produce a TP matrix is a technique that follows the simple diagram

This “exterior bordering” technique represents a strategy for extending ...

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