How to Detect and Construct N-matrices

preprint2020arXivOpen access

N-matrices are real $n\times n$ matrices all of whose principal minors are negative. We provide (i) an $O(2^n)$ test to detect whether or not a given matrix is an N-matrix, and (ii) a characterization of N-matrices, leading to the recursive construction of every N-matrix.

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How to Detect and Construct N-matrices

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