The Nearest Zero Eigenvector of a Weakly Symmetric Tensor from a Given Point
We begin with a degree <i>m</i> real homogeneous polynomial in <i>n</i> indeterminants and bound the distance from a given <i>n</i>-dimensional real vector to the real vanishing of the homogeneous polynomial. We then apply these bounds to the real homogeneous poly...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/5/705 |
| _version_ | 1797264149804220416 |
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| author | Kelly Pearson Tan Zhang |
| author_facet | Kelly Pearson Tan Zhang |
| author_sort | Kelly Pearson |
| collection | DOAJ |
| description | We begin with a degree <i>m</i> real homogeneous polynomial in <i>n</i> indeterminants and bound the distance from a given <i>n</i>-dimensional real vector to the real vanishing of the homogeneous polynomial. We then apply these bounds to the real homogeneous polynomial associated with a nonzero <i>m</i>-order <i>n</i>-dimensional weakly symmetric tensor which has zero as an eigenvalue. We provide “nested spheres” conditions to bound the distance from a given <i>n</i>-dimensional real vector to the nearest zero eigenvector. |
| first_indexed | 2024-04-25T00:24:19Z |
| format | Article |
| id | doaj.art-5963939575934a5592610c33903758e3 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-04-25T00:24:19Z |
| publishDate | 2024-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-5963939575934a5592610c33903758e32024-03-12T16:50:01ZengMDPI AGMathematics2227-73902024-02-0112570510.3390/math12050705The Nearest Zero Eigenvector of a Weakly Symmetric Tensor from a Given PointKelly Pearson0Tan Zhang1Department of Mathematics and Statistics, Murray State University, Murray, KY 42071, USADepartment of Mathematics and Statistics, Murray State University, Murray, KY 42071, USAWe begin with a degree <i>m</i> real homogeneous polynomial in <i>n</i> indeterminants and bound the distance from a given <i>n</i>-dimensional real vector to the real vanishing of the homogeneous polynomial. We then apply these bounds to the real homogeneous polynomial associated with a nonzero <i>m</i>-order <i>n</i>-dimensional weakly symmetric tensor which has zero as an eigenvalue. We provide “nested spheres” conditions to bound the distance from a given <i>n</i>-dimensional real vector to the nearest zero eigenvector.https://www.mdpi.com/2227-7390/12/5/705tensor eigenvalueshigher order tensor |
| spellingShingle | Kelly Pearson Tan Zhang The Nearest Zero Eigenvector of a Weakly Symmetric Tensor from a Given Point Mathematics tensor eigenvalues higher order tensor |
| title | The Nearest Zero Eigenvector of a Weakly Symmetric Tensor from a Given Point |
| title_full | The Nearest Zero Eigenvector of a Weakly Symmetric Tensor from a Given Point |
| title_fullStr | The Nearest Zero Eigenvector of a Weakly Symmetric Tensor from a Given Point |
| title_full_unstemmed | The Nearest Zero Eigenvector of a Weakly Symmetric Tensor from a Given Point |
| title_short | The Nearest Zero Eigenvector of a Weakly Symmetric Tensor from a Given Point |
| title_sort | nearest zero eigenvector of a weakly symmetric tensor from a given point |
| topic | tensor eigenvalues higher order tensor |
| url | https://www.mdpi.com/2227-7390/12/5/705 |
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