کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8897752 | 1631041 | 2018 | 25 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The product of the eigenvalues of a symmetric tensor
ترجمه فارسی عنوان
محصول مقادیر ویژه یک تانسور متقارن
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
We study E-eigenvalues of a symmetric tensor f of degree d on a finite-dimensional Euclidean vector space V, and their relation with the E-characteristic polynomial of f. We show that the leading coefficient of the E-characteristic polynomial of f, when it has maximum degree, is the (dâ2)-th power (respectively the ((dâ2)/2)-th power) when d is odd (respectively when d is even) of the QË-discriminant, where QË is the d-th Veronese embedding of the isotropic quadric QâP(V). This fact, together with a known formula for the constant term of the E-characteristic polynomial of f, leads to a closed formula for the product of the E-eigenvalues of f, which generalizes the fact that the determinant of a symmetric matrix is equal to the product of its eigenvalues.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 554, 1 October 2018, Pages 224-248
Journal: Linear Algebra and its Applications - Volume 554, 1 October 2018, Pages 224-248
نویسندگان
Luca Sodomaco,