An elementary proof of Chollet’s permanent conjecture for 4 × 4 real matrices
A proof of the statement per(A ∘ B) ≤ per(A)per(B) is given for 4 × 4 positive semidefinite real matrices. The proof uses only elementary linear algebra and a rather lengthy series of simple inequalities.
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2021-01-01
|
| Series: | Special Matrices |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/spma-2020-0126 |
| _version_ | 1818676445418881024 |
|---|---|
| author | Hutchinson George |
| author_facet | Hutchinson George |
| author_sort | Hutchinson George |
| collection | DOAJ |
| description | A proof of the statement per(A ∘ B) ≤ per(A)per(B) is given for 4 × 4 positive semidefinite real matrices. The proof uses only elementary linear algebra and a rather lengthy series of simple inequalities. |
| first_indexed | 2024-12-17T08:43:35Z |
| format | Article |
| id | doaj.art-e017fa3f8f3c403d8cdb939d7a8fd906 |
| institution | Directory Open Access Journal |
| issn | 2300-7451 |
| language | English |
| last_indexed | 2024-12-17T08:43:35Z |
| publishDate | 2021-01-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Special Matrices |
| spelling | doaj.art-e017fa3f8f3c403d8cdb939d7a8fd9062022-12-21T21:56:15ZengDe GruyterSpecial Matrices2300-74512021-01-01918310210.1515/spma-2020-0126An elementary proof of Chollet’s permanent conjecture for 4 × 4 real matricesHutchinson George0Department of Mathematical Sciences, Lakehead University, Thunder Bay, Ontario, P7B 5E1, CanadaA proof of the statement per(A ∘ B) ≤ per(A)per(B) is given for 4 × 4 positive semidefinite real matrices. The proof uses only elementary linear algebra and a rather lengthy series of simple inequalities.https://doi.org/10.1515/spma-2020-0126chollet conjecturepositive semidefinite matriceshadamard productmatrix permanent15a1515b48 |
| spellingShingle | Hutchinson George An elementary proof of Chollet’s permanent conjecture for 4 × 4 real matrices Special Matrices chollet conjecture positive semidefinite matrices hadamard product matrix permanent 15a15 15b48 |
| title | An elementary proof of Chollet’s permanent conjecture for 4 × 4 real matrices |
| title_full | An elementary proof of Chollet’s permanent conjecture for 4 × 4 real matrices |
| title_fullStr | An elementary proof of Chollet’s permanent conjecture for 4 × 4 real matrices |
| title_full_unstemmed | An elementary proof of Chollet’s permanent conjecture for 4 × 4 real matrices |
| title_short | An elementary proof of Chollet’s permanent conjecture for 4 × 4 real matrices |
| title_sort | elementary proof of chollet s permanent conjecture for 4 4 real matrices |
| topic | chollet conjecture positive semidefinite matrices hadamard product matrix permanent 15a15 15b48 |
| url | https://doi.org/10.1515/spma-2020-0126 |
| work_keys_str_mv | AT hutchinsongeorge anelementaryproofofcholletspermanentconjecturefor44realmatrices AT hutchinsongeorge elementaryproofofcholletspermanentconjecturefor44realmatrices |