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I am trying to find an $n \times m$ fat (i.e., $m > n$) matrix $T$ that solves $$T^T T = X$$ where $X$ is a given $m \times m$ symmetric, positive semidefinite matrix. I saw this post, but ...

I am interested in solving the following quadratic equation: $$x^{\top} A x = \sqrt{x^{\top} B x}$$ Here, $x \in \mathbb{R^q}$ is an unknown vector, and A and B are two q$\times$q-dimensional ...

Scenario I have a equation for a covariance matrix ${\Sigma}$ where everything but a vector of correlations is known aka $x=(x_{1}, \dots, x_{D})$ for $x_{i}\in [-1, 1]$. Problem I know that ${x}$ ...