A revisit to inertia of the matrices of the type $$[(q_i+q_j)^r]$$ and $$\left[ \frac{{q_i}^{r+1}-{q_j}^{r+1}}{q_i-q_j}\right] $$
Tóm tắt
For given real numbers
$$00,$$
the inertia of the matrix
$$L_{r+1}=\left[ \frac{{q_i}^{r+1}-{q_j}^{r+1}}{q_i-q_j}\right] $$
was studied by Bhatia, Friedland and Jain, which surprisingly came out to be same as that of the matrix
$$P_r=[(q_i+q_j)^r].$$
They left therein with a question about the reason behind the same inertia. We aim to answer this question while revisiting the inertia of these matrices simultaneously.
Tài liệu tham khảo
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