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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How to get non-negative solutions to matrix in R?

I am trying to solve the equation AX = B in R. I have two matrices, A and B: ...
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Scaling Variance-Covariance Matrix of daily returns to quarterly

I am trying to convert my variance-covariance computation, which is based on daily returns of 700 points of data, into a different scale/time period. I am trying to basically have the computed result ...
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17 views

Matrix Calculations and Multivariate Bayesian Methods

Suppose I have the matrix given by: $$X = \begin{bmatrix}1 & 0 & 0\\ 1 & 1 & 0 \\ 1 & 1 & 1 \end{bmatrix}$$ This matrix actually represents whether a user interacted with a ...
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51 views

Latent Semantic Analysis- Theme extraction [closed]

I have a large collection of text documents I am trying to group using Singular Value Decomposition for dimension reduction(popularly known as LSA) followed by k-means clustering. To be able to ...
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21 views

Summation constraint matrix

I'm trying to create an assignment script using the R package Rsymphony, but I can't seem to figure out how to convert the summations into an actual constraint matrix. I tried to figure it out based ...
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59 views

Calculate matrix exponential without dedicated software package [closed]

Is it possible to determine the exponential of a square (non-diagonalizable) matrix without a dedicated package: for example, through a series of equations within a spreadsheet?
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43 views

Help understanding p-vector language

Help interpreting this excerpt (annotations (numbers in parentheses) and bullets added) from The Elements of Statistical Learning Matrices are represented by bold uppercase letters; for example, a ...
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34 views

computation of square root of matrix

I am studying the Canonical correlation analysis(CCA) the formula https://en.wikipedia.org/wiki/Canonical_correlation is involving the -1/2 degree of a matrix. My question is: how can i do the ...
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33 views

Asymmetric matrix in Mantel test?

Does anyone know how to set up an asymmetric matrix to do a Mantel test? The reading I've done says the Mantel stat can be calculated from these matrices, but all packages/programs that I use to run ...
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41 views

Doing a “linear regression” with 2d points under a linear transformation

Let's say I have a list of 2D points $\vec v_i = (x_i,y_i)$ and the list of points after some linear transformation $\vec v_i'= A\vec v + b + \epsilon_i$ where $\epsilon_i$ is some deviation assumed ...
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In linear regression, is there any meaning for the term $X^Ty$?

Recently, I was wondering about this question. In a standard linear regression problem ($y=X\beta$ and we solve for $\beta$), the solution is $\beta = X^{-1}y$ when $X$ is square and invertible, and $...
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Is it legit to run clustering on MDS result of a distance matrix?

I am new to the topic of clustering and face the following problem: I have multiple binary datasets with 10k to 40k entries and 135 features each: $$ \begin{matrix} \newcommand{\feat}{\text{feat}} \...
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What is an example of perfect multicollinearity?

What is an example of perfect collinearity in terms of the design matrix $X$? I would like an example where $\hat \beta = (X'X)^{-1}X'Y$ can't be estimated because $(X'X)$ is not invertible.
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Difference between Residual and Disturbance (epsilon)

Following is a note from page 1 in: Matrix OLS Make sure that you are always careful about distinguishing between disturbances ($\epsilon$) that refer to things that cannot be observed and ...
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10 views

Elements-wise matrix algebra in R arrays [migrated]

I have two arrays with dimensions: arry1[2,2,n] and array2[2,2,n]. That is, n two by two matrices. I want to produce a third array which is the n-element-wise matrix multiplication (i.e., %*%) of ...
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5 views

Missing IV data in MRQAP analyses?

I am attempting to run a multiple QAP regression analyses, to test whether certain social network properties predict the way children solve problems. The DV is binary (do children solve a problem ...
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16 views

Measuring the spread of values in a matrix

Given the following matrices: Matrix 1: \begin{bmatrix}1&1&1\\1&1&1\\1&1&2\end{bmatrix} Matrix 2: \begin{bmatrix}0&0&5\\0&5&0\\0&0&0\end{bmatrix} ...
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78 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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66 views

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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30 views

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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31 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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49 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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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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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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32 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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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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11 views

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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51 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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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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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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49 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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129 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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16 views

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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22 views

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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6 views

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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12 views

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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82 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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24 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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160 views

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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14 views

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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31 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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51 views

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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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\\...