# Tagged Questions

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### Math issue implementing an invoice API [on hold]

Okay, so, I have $2$ separate systems: An invoice record database on an external site, I do not have access to the code here. An prestashop e-commerce installation, where i am developing a plugin. ...
42 views

### Jacobian for a matrix transformation: Example of Cholesky decomposition

I would like to generally understand how the Jacobian of a matrix transformation can be computed. As a concrete example, consider the Transformation from a (correlation) matrix to its Cholesky ...
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### If $A \succeq B$ is it true that $B^{-1} \succeq A^{-1}$

If $A$ and $B$ are two positive definite matrices such that $A - B$ is nonnegative definite, is it true that $B^{-1} - A^{-1}$ is positive definite? The doubt came to me when working with confidence ...
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### Projection equation

I'm a programmer, not a math expert or statistician by any means, but my organization wants a page in our admin console that displays a projection of how many registrations we can expect to see based ...
33 views

### Bayesian linear regression cost function

I am studying classification using linear regression . Now, I want to map it in Bayesian regression. Let talk about binary classification using linear regression again. Assume that I have a set ...
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### Fast way to inverse B'CB+D

$\mathbf {A = B'CB}$, where $\mathbf A$ is of dimension $n \times n$, $\mathbf C$ is m by m, positive definite and symmetric, $\mathbf B$ is of dimension $m \times n$, and $n >> m$. Inversion ...
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### Does affine equivariance implies shape unbiasedness?

Basically, I'm dealing with an algorithm that, given an $n\times p$ data matrix $\pmb X$ with iid rows, returns $\hat{\pmb\sigma}(\pmb X)\in\mathbb{R}^{p\times p}$. To simplify things, I will also ...
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### Understanding details of PCA - variance

I am currently reading through Principal Component Analysis, Second Edition and came to small paragraph that I do not fully understand on page 5 (Section 1.1): "To derive the form of the PCs, ...
32 views

### Strong duality in trace maximization

I'm working on understanding the derivation of the solution for principal components analysis. Let $\mathbf{S} \in \mathbb{R}^{p \times p}$ be a positive semi-definite matrix with rank $d < p$. ...
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### Relationship between the singular value decomposition (SVD) and the principal component analysis (PCA). A radical result(?)

I was wondering if I could get a mathematical description of the relationship between the singular value decomposition (SVD) and the principal component analysis (PCA). To be more specific I have ...
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### connection between PCA and linear regression

Is there a formal link between linear regression and PCA? The goal of PCA is to decompose a matrix into a linear combination of variables that contain most of the information in the matrix. Suppose ...
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### How can solve this integral

How ı can solve this integral, ı thınk that ı can seperate as above ı did but I dıd not do it, thanks for helping..
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### An equation related to covariance matrix, square root of the matrix, and Euclidean norm.

How can I prove this equation: $${ ({ x }^{ T }\Sigma x) }^{ 1/2 }={ \left\| { \Sigma }^{ 1/2 }x \right\| }_{ 2 }$$ In which $\Sigma$ is a covariance matrix. I tried some numerical examples in ...
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### Differentiability of linear least squares

Show that least-squares $\|y-X\beta\|^2$ is twice differentiable and has minimizer. I understand that the second derivative is $X'X$. Also it is a composition of linear function which is ...
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### Avoid dividing by zero with just variables and basic operators

I am working on stats for a sports team, and one of the stats I have the ratio of Shots and Shots on Target (Which I call ...
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### Solving an system of equations for the system

I'm trying to find a $n \times n$ matrix $A$, that satisfies $V_x = A V_y$, where $V_x$ and $V_y$ are both $n \times 1$ vectors of known quantities. For what its worth, the sum of $V_x$ and the sum ...
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### What type of formula am I looking for?

Let say you have a list of items with 3 columns, two are statistical the third is just a name. The statistical categories you have are Points, and Salary. You have 10 different options. Each Row ...
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### How does SVD work?

Trying to find information, and, no-one seems to know the answers. I have a time-series, represented by $T = [0, 1, 1, 0, \ldots, n]$ the time series is then transformed into the Spectral results: ...
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### Algebraically expanding this function

I have an algebra question. I am currently working on this function: $$\left(\frac{{e^{t\sqrt{3/n}}} -{e^{-t\sqrt{3/n}}}}{2t\sqrt{3/n}}\right)^n$$ Now this is the MGF of a function called $Z$ and I ...