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I'm trying to work out a proof for the following proposition: Let $A \in \mathbb{R}^{n,n}$ a real, symmetric matrix with eigenvalues $\lambda_1 \ge \lambda_2 \ge \cdots \ge \lambda_n$, then $$\max \...

Let $A$ and $B$ be two matrices with $\det(A)=\det(B)=1$. Does it follow that $\sqrt{\mathrm{tr}(A^TB^TBA-I)}\le\sqrt{\mathrm{tr}(A^TA-I)}+\sqrt{\mathrm{tr}(B^TB-I)}$ I suspect that this can be ...