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Volume 19, Issue 4
On the Estimations of Bounds for Determinant of Hadamard Product of H-Matices

Yao-Tang Li & Ji-Cheng Li

J. Comp. Math., 19 (2001), pp. 365-370.

Published online: 2001-08

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  • Abstract

In this paper, some estimations of bounds for determinant of Hadamard product of $H$-matrices are given. The main result is the following if $A = (a_{ij})$ and $B=(b_{ij})$ are nonsingular $H$-matrices of order $n$ and $∏^n_{i=1}a_{ii}b_{ii} ＞ 0,$ and $A_k$ and $B_k, k=1, 2, \cdots, n,$ are the $k \times k$ leading principal submatrices of $A$ and $B$, respectively, then 

image.png

where $M(A_k)$ denotes the comparison matrix of $A_k$.

  • Keywords

$H$-matrix, Determinant, Hadamard product.

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-19-365, author = {Li , Yao-Tang and Li , Ji-Cheng}, title = {On the Estimations of Bounds for Determinant of Hadamard Product of H-Matices}, journal = {Journal of Computational Mathematics}, year = {2001}, volume = {19}, number = {4}, pages = {365--370}, abstract = {

In this paper, some estimations of bounds for determinant of Hadamard product of $H$-matrices are given. The main result is the following if $A = (a_{ij})$ and $B=(b_{ij})$ are nonsingular $H$-matrices of order $n$ and $∏^n_{i=1}a_{ii}b_{ii} ＞ 0,$ and $A_k$ and $B_k, k=1, 2, \cdots, n,$ are the $k \times k$ leading principal submatrices of $A$ and $B$, respectively, then 

image.png

where $M(A_k)$ denotes the comparison matrix of $A_k$.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8989.html} }
TY - JOUR T1 - On the Estimations of Bounds for Determinant of Hadamard Product of H-Matices AU - Li , Yao-Tang AU - Li , Ji-Cheng JO - Journal of Computational Mathematics VL - 4 SP - 365 EP - 370 PY - 2001 DA - 2001/08 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8989.html KW - $H$-matrix, Determinant, Hadamard product. AB -

In this paper, some estimations of bounds for determinant of Hadamard product of $H$-matrices are given. The main result is the following if $A = (a_{ij})$ and $B=(b_{ij})$ are nonsingular $H$-matrices of order $n$ and $∏^n_{i=1}a_{ii}b_{ii} ＞ 0,$ and $A_k$ and $B_k, k=1, 2, \cdots, n,$ are the $k \times k$ leading principal submatrices of $A$ and $B$, respectively, then 

image.png

where $M(A_k)$ denotes the comparison matrix of $A_k$.

Li , Yao-Tang and Li , Ji-Cheng. (2001). On the Estimations of Bounds for Determinant of Hadamard Product of H-Matices. Journal of Computational Mathematics. 19 (4). 365-370. doi:
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