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The question is an extention to the answered question prove spectral equivalence bounds for fractional power of matrices. Let $A, D \in \mathbb{R}^{n \times n}$ be two symmetric,positive definite and ...

Let $A, D \in \mathbb{R}^{n \times n}$ be two symmetric,positive definite and tri-diagonal matrices for that we know that they are spectrally equivalent, thus ist holds $$ c^- x^\top D x \le x^\top A ...

Let $A,D \in \mathbb{R}^{n\times n}$ be two positive definite matrices given by $$ D = \begin{bmatrix} 1 & -1 & 0 & 0 & \dots & 0\\ -1 & 2 & -1 & 0 & \dots & 0\\...

Sutter et al. [1] in their paper "Multivariate Trace Inequalities" give an intuitive proof of the following Golden-Thompson inequality: For any hermitian matrices $A,B$: $$ \text{tr}(\exp{(A+B)}) \...

Denote the eigenvalues of an $n\times n$ matrix $\mathbf{X}$ by $\lambda_i(\mathbf{X})$ and its singular values by $\sigma_i(\mathbf{X})$, $i=1,\ldots,n$. When $\mathbf{X}$ is Hermitian, we know that $...