Questions tagged [matrix]

A matrix (plural matrices) is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. The individual items in a matrix are called its elements or entries.

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Proof $E[Z'TZ]^2=\operatorname{tr}^2(T)+\operatorname{tr}(T^2)$ [duplicate]

How to prove second moment of a quadratic form where $Z$ has normal distribution with mean zero and covariance matrix identical?
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Maximizing Sum of Upper Triangle Matrix Elements with Respect to Column and Row Swapping

So, I wanna make a ranking method for teams in the EPL, there are 20 teams in EPL, therefore there are $20!$ configurations of ranking assignment, my final ranking assignment would be the one that ...
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I am writing this question seeking some help with an elegant, inline solution to stack matrices and at each iteration in the stack, apply a power. I have two matrices \Lambda \in \mathbb{R}^{m\... 0answers 21 views Question about collinearity amongst variables in a correlation matrix I have a data set which contains cell counts across the 250 brain regions in 12 animals. I want to construct a correlation matrix and a graph theoretical model using the grouped lasso correction. ... 1answer 92 views When does the underfitted regression model have more precise coefficient estimates? Say we have a full regression model \begin{align*} \mathbf{y} &= \mathbf{X} \boldsymbol{\beta} + \boldsymbol{\epsilon}\\ &= \mathbf{X}_p \boldsymbol{\beta}_p + \mathbf{X}_r \boldsymbol{\beta}... 1answer 27 views representation of a convolutional layer as a fully connected one (matrix representation) I'm surprised this isn't a duplicate, but Google seems to confirm that this is indeed the case. What is the representation of a convolutional layer as a fully connected layer? A convolutional layer ... 0answers 14 views How to apply the diffusion maps when the matrix is PSD but not positivity preserving? In order to apply the diffusion maps in a matrixC\in\mathbb R^{n\times n}$, that matrix must obey some restrictions, C is symmetric:$C_{ij} = C_{ji}$, C is positivity preserving (PP):$\forall ...
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Below is the weight matrix of a Hopfield network ...
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Gradient Descent Vectorization with Numpy (1D transpose confusion) [closed]

I'm working through Andrew Ng's original Stanford course and ran into some numpy confusion. Basically, my main question is, if we dot product a 1D array with a 2D array in numpy (and the dimensions ...
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Is “$\mathrm E[X'X]$ has rank $k$” the assumption of no multicollinearity?

My lecturer wrote this on the board: Assume $\mathrm E[X'X]=Q$ has rank $k$, where $X$ is the data matrix and $k$ is the number of independent variables. I asked her if that is the assumption of ...
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Use a Mantel test in R

I have two matrices, which are exactly the same ones. I apply a mantel test and I get this output : ...
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Kappa condition number in R

I have read that the kappa function in R does not always explicitly calculate the condition number of a matrix, but rather, estimates the 2 norm of a matrix or a QR ...
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Updating regression solutions for removing a regressor without the original dependent variable

Note: This question is analagous to the question I asked here except instead of adding a column, I am removing it. I am interested in a linear regression on the model; $Y= X\beta + \epsilon$ And I ...
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Verifying Identification Results for Univariate Regression

So I have this linear regression model shown below and I'm supposed to be showing that equation 3 is equal to equation 4. There's a hint that says a 2x2 inverse matrix appears in the proof, but the ...
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Is it useful to add a proportion hyperparameter in the concatenation layer?

I'm reading a paper on deep learning-based recommender systems: Neural Collaborative Filtering. There are two sub-networks, GMF and MLP, which are fused into a unified model, by a concatenation layer. ...
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Dimensionality of similarity matrix

Below is a screen shot of a paper. The authors take a data-set $E\in R^{nxm}$. Here $n$ is the number of observations/samples/patients and $m$ is the number of genes/features. Preprocessing ...
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What is the most intuitive proof that Gaussian kernel is positive definite?

I have general form of Gaussian kernel $K(x,x')=\exp(-\|x-x'\|^{2})$ (just not considering $\sigma$). I tried to prove its positive definiteness via Gram matrix properties, but couldn't. Is there any ...
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adding a small constant to the diagonals of a matrix to stabilize

I have a large correlation matrix (110x110) with some small eigenvalues (about 20 < 0.1). It has been suggested that adding a constant (about 0.1) to the diagonals will help to stabilize the matrix....
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Build customer ratings from subscription datetime data for a recommendation system

I want to build a recommendation system with only some customer's subscription and unsubscription date. I have a database that looks like: ...
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Measure the change of feature set over time

I have two matrices mat1 and mat2, the same number of columns but the different number of rows. You can imagine that ...
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What is the Joint Density Function of a Three-Level Mixed-Effects Model?

This is a follow-up question to a question I posted earlier. Obviously, maximum-likelihood estimation of mixed-effects models requires the joint density function. Let us assume a two-level mixed ...