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Amin
Amin
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Suppose $A$ is a positive semi-definite matrix and we can bound its trace as $l \le tr(A) \le L$. I am wondering if it is possible to find the upper and lower bounds on the trace of $A^{-1}$ based on $tr(A)$ and its bound? What inequalities hold and under what conditions?

Edit: I should add that there is a lower bound for eigenvalues of the matrix $A$, i.e., $\lambda_i(A)\ge \lambda_0$.

Thanks

Suppose $A$ is a positive semi-definite matrix and we can bound its trace as $l \le tr(A) \le L$. I am wondering if it is possible to find the upper and lower bounds on the trace of $A^{-1}$ based on $tr(A)$ and its bound? What inequalities hold and under what conditions?

Thanks

Suppose $A$ is a positive semi-definite matrix and we can bound its trace as $l \le tr(A) \le L$. I am wondering if it is possible to find the upper and lower bounds on the trace of $A^{-1}$ based on $tr(A)$ and its bound? What inequalities hold and under what conditions?

Edit: I should add that there is a lower bound for eigenvalues of the matrix $A$, i.e., $\lambda_i(A)\ge \lambda_0$.

Thanks

Source Link
Amin
Amin
  • 111
  • 3

Bound on the trace of inverse matrix

Suppose $A$ is a positive semi-definite matrix and we can bound its trace as $l \le tr(A) \le L$. I am wondering if it is possible to find the upper and lower bounds on the trace of $A^{-1}$ based on $tr(A)$ and its bound? What inequalities hold and under what conditions?

Thanks