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Given a matrix $A \in \mathbb{R}^{n\times m}$, and its perturbation $$ A_p = A + \Delta $$ is there a way to represent $$ (A_p)^{\star}= (A)^{\star} + f(\Delta) $$ where $(A_p)^{\star}$ ($(A)^{\star …

I am trying to understand Wedin Theorem on the perturbations of the Singular Vectors of a matrix, and a key element for this theorem is the matrix of the canonical angles between two subspaces; I am m …

I have a real matrix $A \in \mathbb{R}^{n\times n}$ such that: $A$ is symmetric All the off-diagonal terms are known and positive Has rank $k<n$ Unfortunately I don't know the values of the diagon …

Given any symmetric real valued matrix $A \in \mathbb{R}^{n\times n}$, I can decompose $A$ as the product of two complex matrices $$ A = E'E $$ Practically this can be done easily using SVD decompos …

Given any $n \times k$ real matrix $M$, where $n<k$ and $rank(M)=n$, I consider the following equation (where $M'$ is the transpose of $M$): $$ MM' = MAM' $$ Then clearly, $A = \mathbb{1}_k $, the $ …