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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Estimation of Large Seemingly Unrelated Regressions Systems [migrated]

I'm using Bayesian methods to estimate a system of Seemingly Unrelated Regressions (SUR). The system I'm estimating, however, is large, and I'm trying to find a computationally feasible way to ...
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What is the most efficient way to create a 'difference matrix' i.e., the difference between each row and all others? [migrated]

I have a square matrix of like this: [[ 1., 2., 3.], [ 4., 5., 6.], [ 7., 8., 9.]] and want a matrix like this: ...
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76 views

How is the principal component applied on to the data?

I am bit unsure (Or might be overthinking this) or is the chosen PC somehow applied on to the data, to reduce the dimentionality of the data, or how does one use PC to do any form of mathematical ...
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What is the probability that the matrix is orthogonal?

Let $X$ and $Y$ be independent $Bin(3,\frac{1}{3})$ random variables. Then what is the probability that the matrix, $$ P=\begin{bmatrix} \frac{X}{\sqrt2}&\frac{Y}{\sqrt2}\\\frac{-1}{\sqrt2}&\...
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Find projection matrix using partitioned matrices

If $X$ is a ($n$, $p+1$) design matrix, partition $X$ to be $X$=[$J$ $X$*] where $J$ is a ($n$,$1$) vector of all $1$'s, and $X$* is a ($n$,$p$) matrix. Let $H_X$ be a projection matrix, where $H_X$...
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How do you correlate two non-square matrices with permutations?

I am having difficulty finding a package or finding code for a permutation test to correlate two non-square matrices. Basically, trying to do a mantel test but for non-square matrices. Any help is ...
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23 views

Fisher information matrix with a general covariance structure

For the linear model, general linear models which allow for a more general covariance structure $V(\theta)_{N\times N}=(I_{N}+\theta A_{N\times N})(I_{N}+\theta A_{N\times N})^{'}$ ,where $A_{N\times ...
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Covariance matrix through bootstrapping - close to zero determinant

I have a set of 260 sets of measurements (for each set of measurements there is an amplitude measured as a function of 8 radii). Since I do not get measurement errors and I am interested in the ...
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1answer
43 views

Sort Table Rows/Columns to Minimize Distance

I am working on a project where I am given a large table of numbers, in which we are hoping to see certain patterns. For example (using R): ...
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How can I add a 2D matrix in R as a dataframe variable? [migrated]

I am trying to use the PLS library in order to run Partial Least Squares Regression. I imported my data from MATLAB with 'R.matlab' library. One of my matrices I managed to insert to a dataframe quite ...
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Chi-square and R: Calculate matrix of statistical significances between results

First of all, I would like to apologize if this is an duplicate of an earlier question. I find it hard to believe that I am the first person to ever have this sort of problem, but I am so far out of ...
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Interpreting the Structure matrix in Discriminant Analysis

I was trying to do a discriminant analysis in SPSS and I have to interpret the output. But when I come to the table of Structure Matrix, I find difficulty in defining the variables I should use in ...
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1answer
46 views

R - Constrained Optimization of a Function with Large Matrix Input Having Both Fixed and Dynamic Variables

I am trying to run an optimization on a ROI function with a large matrix (~9,000 rows and 15 columns) as an input. A sample of my data structure is below: ...
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14 views

SVD - collaborative based filtering - Prediction matrix

On the movielens dataset, I used SVD to find U, s, and V matrices. Then performed the dimensional reduction by elimination of everything corresponding to lower valued eigen values( upto a threshhold). ...
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31 views

Understanding Matrix and Vector Notation

I am trying to understand the Matrix and Vector Notations on page 2 here: (the page is also pasted below, to make it easier to explain the problem). Problem: For equation (2), I think it should be $\...
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6 views

Tunable sparsity parameter in sparse matrix approximation

I'm mostly casting around for what terms I should be looking for in the literature, but specific recommendations are also welcome. I have a sparse binary matrix in a collaborative filtering scenario. ...
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Correlate two matrix representing different variables

I've two matrix containing informations from 50 samples and 20000 genes. Matrix A contains the gene expression; Matrix B the methylation state of these genes. My first idea was to compute the ...
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1answer
50 views

What can I do with NA values in my second-order Markov chain?

I have states A, B, C, I have developed both a 1st and 2nd Order Markov Chain for them. Each state represents a status that an individual can be in, and the transitions represents the probability of ...
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2answers
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Which of the 3 cases should my data matrix belong to ideally?

I found this question, and while useful, I wanted to ask something more spcific: I am trying to get a good handle/intuition for the two types of data dimensionalities (number of data samples, and the ...
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1answer
30 views

Distribution of the product of a Wishart matrix

If $\mathbf{M} \sim W_2(\Sigma, 3)$ is a Wishart matrix and $\Sigma =\begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix}$ then what is the distribution of $(3, 1) \mathbf{M}^{-1}(3,1)^T$ ? Thank ...
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29 views

Creating a Radial basis function kernel matrix in matlab

I never used matlab, and I have this code about kernalized locality sensitive functions. I think that the following code is trying to create the kernalized matrix of a RBF kernel function: ...
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Find out a huge number of coordinates is uniformly distributed or not

Assume that we have a huge number of locations like $10^{6}$ locations in two-dimensional space. The coordinates are generated randomly. what I want to do is to make sure that the data distributed ...
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92 views

What is the difference between the anti-image covariance and the anti-image correlation?

What is the difference between the anti-image covariance and the anti-image correlation? How are the matrices of these coefficients computed, and what is the meaning of their elements?
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matrix signal deconvolution

I measured the dietary habits of thousands of animals throughout the world, giving me the following matrix: X = (M x N), where Xij = measurement of food j in animal i M = number of animals N = ...
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How to design a contrast matrix with a continuous variable

I was wondering if someone could help me designing a contrast matrix when you have a continuous variable. My model looks like this: ...
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1answer
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constructing random effects design matrices for lassop{MMS}

I'd like to use elastic net regression for coefficient estimate and parameter selection on a data set that includes nested structure. I've been experimenting with lassop{MMS} to do so. I'm not a ...
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generating random matrix

My problem is this: I have a matrix with three columns. I created a second matrix with only two columns where column1 is the first column (col1) from the first matrix and column2 = 0.01*col1*col2*col3....
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Using a change detection error matrix approach for raster aggregation

I am assessing annual land use change along a 10 year period and have rasterized a vector land use dataset to base resolution 'n' metres to do so (vector data is taken as ground truth, errors in it ...
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Simultaneously Diagonalizable matrices

I'm interested in partitioning matrices into groups which are almost simultaneously diagonalizable. I'm aware that if matrices commute and one of them has no multiple eigenvalues then the matrices are ...
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Interpreting the psych::cor.smoother function in R

I've tried to contact William Revelle (the package creator) about this but he isn't responding. In the psych package there is a function called cor.smoother, which determines whether or not a ...
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1answer
57 views

Neural Net Matrix Multiplication

I'm trying to figure out the matrix multiplications for the implementation of a single hidden layer neural net for MNIST digit recognition in Python. Like the following: ...
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1answer
21 views

$LDL^T$ decomposition from Cholesky decomposition

Suppose we have a covariance matrix $\Sigma$. I know that the Cholesky decomposition $A^T A$ can be found from the LDL decomposition using $$ \Sigma = LDL^T = (LD^{\frac 1 2})(LD^{ \frac 1 2 })^T = A^...
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Decrease of $(X'X)^{-1}$ as n increases

Let $X$ be a $n \times p$ matrix ($n \geq p$ like a conventional data matrix), with each column j filled by iid draws from a variable $\mathcal{X}_j$. I would like ...
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Several variables in correlation matrix output

I'd like to improve a big correlation matrix output correla, because I want to see significante values (p<0.05) but with my code is very dificult to find ...
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29 views

How does Guttman's image analysis work?

Could anyone explain to me how Guttman's image matrix works? Is extracting variables a reiterative process? Are all variables extracted? What's the meaning of the formula? What happens to the diagonal ...
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Variance of a multivariate AR(1) process

I have a multivariate AR(1) process (first-order vector autoregression, VAR(1)) of the form $$ \pmb X_{t+1} = A \pmb X_t + \zeta_t $$ where $\pmb X_t$ is a vector, $A$ is a matrix and $\zeta_t \sim N(...
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1answer
126 views

Codification of Matrix $X$ in $Y=XB+\epsilon$

The variables for the data below is age, group (treatment 1,2,3), Y response variable. \begin{bmatrix}60&1&5.5\\57&2&4.5\\59&3&8.1\\68&1&0.6\\67&2&1.9\\...
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1answer
47 views

Recommenderlab not working with highly sparse binary data?

The data used is a ratings matrix generated from simple 0-1 yes/no click data based on whether or not a user visited a section of a website. This is implicit voting since if a user is interested in a ...
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73 views

Differentiating the RSS w.r.t. $\beta$ in Linear Model

I am reading the book "The Elements of Statistical Learning". The book says But when I try to prove it, I get the following: $$RSS(\beta) = (y - X\beta)^T(y-X\beta)$$ $$RSS(\beta) = y^Ty -\beta^TX^...
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42 views

How to obtain the inverse of a matrix while solving an equation?

Given a matrix $A$, let us assume there is a equation: $Ax = b$ To solve for $x$, we can write: $x = A^{-1} b$ One way to obtain the inverse of A is by single value decomposition: Decomposition ...
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R-programming limma design matrices

I have a really basic understanding of how the package limma works in that it fits a linear model to each row/sample in a micro-array dataset. What I do not understand is how to use a design matrix to ...
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How to provide input to TSNE

I am using TSNE for the first time for dimension reduction. I have around 12 million records with 5000 distinct values. I want to perform dimension reduction (DR) so that I visualized those distinct ...
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When using loss matrix in rpart in R, xerror does not start at 1 [closed]

I am trying to use a loss matrix in rpart penalizing false positives 10 times as much as false negatives, but when I fit my data and then use printcp, my xerror values start at 10 and not 1. I am ...
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How to find the generalized inverse of a matrix in SageMath?

Given a matrix $A_{m\times n}$, a matrix $G_{n\times m}$ is said to be a generalized inverse of $A$, if it satisfies, $$AGA=A$$ Now, since for a matrix $A$, generalized inverse of $A$ is plenty if ...
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1answer
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Question about idempotent matrix: how can M(I-M) equal zero?

Let me assume that M is an idempotent matrix (MM=M) and (I-M) is not zero (I is identity matrix with the same dimensions as M). If I multiply (I-M) by M, (M-MM)=(M-M)=0. How could it be possible that ...
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Get distance matrix directly condensed

I am developing a content-recommender Python system and most of my items (~8 millions) are static so I have thought about pre-computing the top 150 similar items for each item. This way, when a user ...
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Confusion Matrix in FCM

I have written code of FCM(Fuzzy c-mean) in java for centroid and membership matrix generation as well as object function. How can i generate confusion matrix any idea in this FCM program.
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Application of Givens rotation to two matrices

I am reading this paper on Multiresolution Matrix Fatorization, http://arxiv.org/pdf/1507.04396v1.pdf, and have come across something that seems like an error to me. In Algorithm 2, the authors take $...
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Input matrix construction for time series

I am having problems constructing the input matrix for a data analysis / machine learning task. The data set consists of ~300 data points, each one in form of a matrix where rows are time steps, ...