M-tensors and The Positive Definiteness of a Multivariate Form

Details M-tensors and The Positive Definiteness of a Multivariate Form M-tensors and The Positive Definiteness of a Multivariate Form

2012-02-29

arxiv.org/abs/1202.6431v1

Mathematics

Numerical Analysis

Scientific paper

We study M-tensors and various properties of M-tensors are given. Specially,
we show that the smallest real eigenvalue of M-tensor is positive corresponding
to a nonnegative eigenvector. We propose an algorithm to find the smallest
positive eigenvalue and then apply the property to study the positive
definiteness of a multivariate form.

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