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I have the following function for two matrices ${\bf A}$ and ${\bf B}$: $f({\bf A}, {\bf B}) = \| {\bf Y - XAB} \|_F^2 = trace\{({\bf Y - XAB)}^T({\bf Y - XAB)}\}$ where matrices ${\bf X}_{n \times ... 2answers 369 views ### An equivalence relation for norms Let us say that two norms$\|\cdot\|_1$and$\|\cdot\|_2$on a real vector space$V$are strongly equivalent if there exists a constant$\lambda \geq 1$such that$$\frac{1}{\lambda} \left( \|x\|_1 ... 1answer 193 views ### About generalized Minkowski inequality For which functions$f:\mathbb{R}^+ \to \mathbb{R}^+$does the inequality$f^{-1}\left(\sum\limits_{k=1}^n f(x_k+y_k)\right) \leq f^{-1}\left(\sum\limits_{k=1}^n f(x_k)\right) + ...
Let $\mathcal{N}_{n}$ be the set of symmetric nonnegative irreducible matrices. For a matrix $A \in \mathcal{N}_{n}$ let $v^{A}$ be its Perron vector, normalized so that $||v^{A}||_{2}=1$. Define the ...
Background: Let $\mathcal{K}$ be set (convex cone, if you like) of symmetric matrices of order $n$. Each matrix $A \in \mathcal{K}$ can be decomposed in a unique way as $A=A_{+}-A_{-}$, where ...