Some Hadamard product inequalities for accretive matrices
In this paper, we obtain some new matrix inequalities involving Hadamard product. Also some Hadamard product inequalities for accretive matrices involving the matrix means, positive unital linear maps and matrix concave functions are investigated. Among other results, it is shown that if $A, B, C, D...
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| creator | Sheikhhosseini, A Malekinejad, S Khosravi, M |
| description | In this paper, we obtain some new matrix inequalities involving Hadamard
product. Also some Hadamard product inequalities for accretive matrices
involving the matrix means, positive unital linear maps and matrix concave
functions are investigated. Among other results, it is shown that if $A, B, C,
D$ are $n\times n$ positive definite matrices, then \begin{equation*}
\left(\alpha A+\beta B\right)^r\circ\left(\alpha C+\beta D\right)^{1-r}\leq
\alpha\left(A^r\circ C^{1-r}\right)+\beta\left(B^r\circ D^{1-r}\right),
\end{equation*} where $r \in (-1, 0) \cup (1, 2)$ and $" \circ "$ stands for
the Hadamard product. |
| doi_str_mv | 10.48550/arxiv.2307.02838 |
| format | Article |
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product. Also some Hadamard product inequalities for accretive matrices
involving the matrix means, positive unital linear maps and matrix concave
functions are investigated. Among other results, it is shown that if $A, B, C,
D$ are $n\times n$ positive definite matrices, then \begin{equation*}
\left(\alpha A+\beta B\right)^r\circ\left(\alpha C+\beta D\right)^{1-r}\leq
\alpha\left(A^r\circ C^{1-r}\right)+\beta\left(B^r\circ D^{1-r}\right),
\end{equation*} where $r \in (-1, 0) \cup (1, 2)$ and $" \circ "$ stands for
the Hadamard product.</description><identifier>DOI: 10.48550/arxiv.2307.02838</identifier><language>eng</language><subject>Mathematics - Functional Analysis</subject><creationdate>2023-07</creationdate><rights>http://creativecommons.org/licenses/by-sa/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2307.02838$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2307.02838$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Sheikhhosseini, A</creatorcontrib><creatorcontrib>Malekinejad, S</creatorcontrib><creatorcontrib>Khosravi, M</creatorcontrib><title>Some Hadamard product inequalities for accretive matrices</title><description>In this paper, we obtain some new matrix inequalities involving Hadamard
product. Also some Hadamard product inequalities for accretive matrices
involving the matrix means, positive unital linear maps and matrix concave
functions are investigated. Among other results, it is shown that if $A, B, C,
D$ are $n\times n$ positive definite matrices, then \begin{equation*}
\left(\alpha A+\beta B\right)^r\circ\left(\alpha C+\beta D\right)^{1-r}\leq
\alpha\left(A^r\circ C^{1-r}\right)+\beta\left(B^r\circ D^{1-r}\right),
\end{equation*} where $r \in (-1, 0) \cup (1, 2)$ and $" \circ "$ stands for
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product. Also some Hadamard product inequalities for accretive matrices
involving the matrix means, positive unital linear maps and matrix concave
functions are investigated. Among other results, it is shown that if $A, B, C,
D$ are $n\times n$ positive definite matrices, then \begin{equation*}
\left(\alpha A+\beta B\right)^r\circ\left(\alpha C+\beta D\right)^{1-r}\leq
\alpha\left(A^r\circ C^{1-r}\right)+\beta\left(B^r\circ D^{1-r}\right),
\end{equation*} where $r \in (-1, 0) \cup (1, 2)$ and $" \circ "$ stands for
the Hadamard product.</abstract><doi>10.48550/arxiv.2307.02838</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Functional Analysis |
| title | Some Hadamard product inequalities for accretive matrices |
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