کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
401590 675389 2013 24 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On determinants and eigenvalue theory of tensors
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر هوش مصنوعی
پیش نمایش صفحه اول مقاله
On determinants and eigenvalue theory of tensors
چکیده انگلیسی

We investigate properties of the determinants of tensors, and their applications in the eigenvalue theory of tensors. We show that the determinant inherits many properties of the determinant of a matrix. These properties include: solvability of polynomial systems, product formula for the determinant of a block tensor, product formula of the eigenvalues and Geršgorinʼs inequality. As a simple application, we show that if the leading coefficient tensor of a polynomial system is a triangular tensor with nonzero diagonal elements, then the system definitely has a solution in the complex space. We investigate the characteristic polynomial of a tensor through the determinant and the higher order traces. We show that the k-th order trace of a tensor is equal to the sum of the k-th powers of the eigenvalues of this tensor, and the coefficients of its characteristic polynomial are recursively generated by the higher order traces. Explicit formula for the second order trace of a tensor is given.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Symbolic Computation - Volume 50, March 2013, Pages 508-531