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.

learn more… | top users | synonyms

0
votes
0answers
10 views

Filling a Matrix on the basis on data in two columns [on hold]

I have a following matrix M - A B C D A 0 0 0 0 B 0 0 0 0 C 0 0 0 0 D 0 0 0 0 and Data Frame - DF C_Name F_Name Sam A Sam D Sam C Tom C Tom ...
0
votes
0answers
4 views

4x4 matrix of 4 time series is singular up to certain, why? [duplicate]

why is a covariance matrix which is calculated from 4 time series, so it is 4x4, singular up to time point i=5? I need to calculate with the determinant which is not availble until i=5 so my ...
0
votes
0answers
19 views

integral of trace function [migrated]

How can I compute the below integral? $$ \int e^{-1/2*tr[(\mu\mu^T-\mu m^T-m\mu^T)\Sigma]}d\mu $$ in which $\mu \in R^{n},m \in R^{n},\Sigma \in R^{n*n}$ and $tr(.)$ is trace of matrix. I have ...
0
votes
0answers
24 views

how to normalize demand/availability matrix for Citibike data

I am not a statistician but would appreciate an outside perspective on my current project analyzing citibike data. This is a bit complicated so please bear with me. My goal is to determine to what ...
0
votes
0answers
4 views

What is the R code to make predictor variables into matrix? [migrated]

What is the R code to make predictor variables into matrix? if: formula = liking ~ moisture + sweetness predictor variables are moisture and sweetness. now I want to calculate the coefficients by ...
1
vote
0answers
40 views

Mean subtraction and addition purpose

I read Efficient and Accurate Approximations of Nonlinear Convolutional Networks paper. I have this point I don't understand in section 2.1. But may be, my question will be more general. it is known ...
0
votes
0answers
11 views

SSCP vs correlation matrix [duplicate]

Lets say I have a matrix X, where each row is a subject and each column is a variable. I have a few questions about manipulating this matrix, and what the result is: If I calculate X'X, am I correct ...
0
votes
0answers
5 views

What does $\bigotimes$ and $X^*$ mean? [migrated]

Can someone explain / link me to a linear algebra worked problem where I can see how these work. I've searched and given their statistics and matrix specialty uses, can't find any ready examples.
0
votes
0answers
10 views

Average distance in distance matrix

I have a set of many longitude and latitude points within a city. I constructed the nxn euclidean distance matrix. My goal is to know which is the average distance ...
1
vote
1answer
22 views

Design matrix with intersec 0 or 1

I am constructing a model matrix for a repeated meassurments experiment with three individuals per group and three treatments per individual. ...
2
votes
1answer
41 views

How to identify if parameters are estimable, after defining a design matrix

I need to define a design matrix $X$ so that it fits this scenario: For $1\leq i< j \leq 5$, where $i$ are competitors and $j$ are different competitors. Their score is $y_{ij} =$ score of player ...
0
votes
0answers
20 views

Linear models with Matrix notation - eigenvalues, eigenvectors and geometric meaning

Find the eigenvalues and the eigenvectors: 1) $ C=\alpha I_n - (1-\alpha)J $, where $J=ii'$, such that $i=(1,1,...,1)' \in \mathbb{R}^n$, and $\alpha \in (0,1)$. 2) $B=I_n - \frac{1}{n}J$. So, ...
0
votes
1answer
37 views

Analysing data from multiple matrices

I have created a function which produces 1000 different matrices simulating the ranking of football teams. The 1000th matrix produced is as so: ...
1
vote
1answer
15 views

“weigh” different variance covarance matrixes

so my question if I have a set of weights which sums to 1 (say: [0.2,0.2,0.6]) which would represent my states of the world and I have forecasted 3 different variance covariance matrixes (all of which ...
0
votes
0answers
10 views

Converting a m x n matrix to a n*m x 3 matrix [migrated]

I currently have a matrix that is 479 x 729, and I would like to convert this matrix into a three column matrix such that the first column is the row entry of the original matrix, the second column is ...
4
votes
3answers
333 views

Matrix inverse not able to be calculated while determinant is non-zero

I was attempting to calculate an OLS regression in R when I saw some strange things. The inverse of a square matrix does not exist if and only if the determinants is 0. Also, the matrix must be of ...
0
votes
1answer
62 views

What is UV decomposition?

As I'm reading about different matrix decomposition methods, I see a reference to a decomposition method that is known as UV method where: U: has small number of columns V: has small number of rows ...
1
vote
0answers
14 views

Computing the covariance matrix in PCA [duplicate]

PCA method finds the covariance between data vectors, where each data vector includes observations of different variables (dimensions). So if the data matrix has variables in columns and observations ...
2
votes
1answer
33 views

“General” normal equations?

I am quite familiar with the usual OLS estimate for $\boldsymbol\beta$, given by $$\hat{\boldsymbol\beta} = (X^{T}X)^{-1}X^{T}\mathbf{Y}$$ for the linear model $\mathbf{Y} = X\boldsymbol\beta + ...
1
vote
1answer
45 views

Markov Cluster Algorithm transition matrix

I am reading the notes on Markov Cluster Algorithm by Kathy Macropol (http://www.cs.ucsb.edu/~xyan/classes/CS595D-2009winter/MCL_Presentation2.pdf) On slide 14/46 the author talks about inflation and ...
0
votes
0answers
29 views

What does the product of the covariance matrix by a metric matrix actually mean?

Let be the following data matrice: $$A=\begin{bmatrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 2 \\ 2 & 1 & 1 \\ 1 & 1 & 0 \\ 2 & 3 ...
0
votes
0answers
28 views

Singular Value Decomposition and Least Squares

From Elements of Statistical Learning (pp. 64, 66), they explain how the $N \times p$ data matrix $X$ can be written as $$X = UDV^{T}$$ Here $U$ and $V$ are $N \times p$ and $p \times p$ ...
0
votes
0answers
21 views

Propagation of error in matrix multiplication involving an inversion

Hi I have a system $a$ = $B^{-1}x$ where $a$ and $x$ are 9x1 vectors and $B$ is a 9x9 matrix to be inverted Each element in $B$ is a product of two values with their own uncertainties and the vectors ...
0
votes
1answer
37 views

Which is the right way to apply PCA on different sized matrices

I am working on human age classification where I have four descriptors, namely GEI, FED, UC ...
0
votes
1answer
65 views

Import external correlation matrix and sample size to run (MA)SEM in Stata

I want to run a meta-analytic structural equation model (MASEM) in Stata. I already have the meta-analytic mean correlation matrix and the sample size for each correlation. Now I want to import this ...
0
votes
0answers
26 views

Granger causality with matrices [duplicate]

I have a short question regarding Granger causality. I understand Granger only intuitively. If I am correct, it happens when $y_{t-1}$ and $x_t$ are better in explaining $y_t$ than only $y_{t-1}$. ...
1
vote
0answers
29 views

Joint PDF (or MGF) of random sums

I am interested in finding the joint PDF of two sums of random variables. Let: $\textbf{Z} = \left[ {\begin{array}{*{20}{c}} {{z_1}} \\ {{z_2}} \end{array}} \right] = \textbf{D}\textbf{X}$ ...
3
votes
0answers
18 views

Sampling vector so they will have a given euclidean distances matrix

Given a matrix $M\in\mathbb{R}^{P\times P}$ , is it possible to sample $P$ vectors $u_i\in\mathbb{R}^N$, $i=1..P$ so that $\|u_i-u_j\|=M_{ij}$. Obviously for not any $M$ this is possible, i.e. it has ...
0
votes
0answers
14 views

Computing design matrix from covariance matrix

Suppose I have the following regression model: $Y = b_1 \times T + b_2 \times Z + b_3 \times T\times Z + \epsilon$ where T is a randomly assigned treatment condition and Z is some covariate. I want ...
0
votes
0answers
25 views

Scatter matrix Sw Sb and St in python

I'm trying to compute the Sw, Sb and St scatter Matrix in python language, But I know that there are library with implementations of scatter matrix for plotting like the following ...
0
votes
0answers
19 views

Write the $X$ matrix and $B$ vector for the models

Write the $X$ matrix and the parameter vector $B$ for the following models, with $i=1,2,3,4$: a)$log(Y_i)=B_0+B_1x_{i1}+B_2X_{i2}+\epsilon_i$ b)$3Y_i=B_0^{x_{i1}}B_1x_{i2}\epsilon_i$ ...
0
votes
1answer
43 views

Least Squares Definition in Elements of Statistical Learning

In Elements of Statistical Learning, they state on p. 11 that all vectors are column vectors and start developing the least squares idea. So if we have $$\mathbf{X} = \begin{bmatrix} 1 \\ X_1 \\ X_2 ...
0
votes
0answers
10 views

When choosing k biggest eigenvalues for dimension reduction, should I take into account the absolute value?

I want to reduce the dimension of a matrix, I want to take K biggest eigenvalues and vectors that represent 98% of the sum of the eigenvalues. Is this sum taking the absolute value of all ...
0
votes
1answer
22 views

the components in the error in x in the damped least square problem

Could someone explain for me why the error in x in the damped least square problem has two components,one from the noise on b and an approximation error from tau.
0
votes
0answers
28 views

Corner Point Constraint

How do you implement the corner point constraint, within a design matrix from a linear regression model? thanks
2
votes
0answers
18 views

writing piecewise regression model as a linear model

lets write the following piecewise regression model $$y= \alpha_0 + \alpha_1 x +\epsilon ;\ \ x\le x_0 $$ $$ y=\beta_0 +\beta_1 x + \epsilon\ \ x\gt x_0$$ according to the variable $x_0$ is known, ...
0
votes
0answers
39 views

How to set up a VECM in R?

I am making a VECM model in R, where I want to know whether or not I have set it up right. My model is as follows: $$ \Delta y_t=\delta + \alpha \beta'y_{t-1} + \Gamma \Delta y_{t-1} + \varepsilon_t ...
0
votes
0answers
19 views

Upper bound on the expected trace of the inverse of a sum of psd matrices

Let $X$ be an $n\times n$ rank-deficient positive semi-definite matrix and let $Y$ be an $n\times n$ full-rank, positive definite matrix. Suppose that $\mathbb E \ \text{tr}(X)$ and $\mathbb E \ ...
0
votes
0answers
49 views

Learning hat matrix

I'm stuck learning the hat matrix and wondered if someone could help with a question. If I have the model $$Y_i =\beta_0+\beta_1X_i+\epsilon_i,i = 1,2,3 \dots n,$$ how can I calculate the hat matrix ...
1
vote
0answers
25 views

Kendall correlation of two linear transformations

Assume we have two $p\times 1$ random, zero-mean vectors $X$ and $Y$ with covariance matrices: $E[XX^T]=Q$ and $E[YY^T]=S$, and also $E[YX^T] = R$. Also, let $B$ be an $n\times p$ matrix. I want to ...
2
votes
1answer
27 views

Is it possible to use a mean squared error for matrices?

Could I use a mean squared error statistical analysis on a set of 1 x 2 matrices? For example, if I had [123 456] as the actual matrix and [111 222] as the predicted matrix, could I use the mean ...
1
vote
0answers
26 views

Linear regression problem with multi-dimensional vectors instead of scalar values as predictions

Goal I have a training set $S$ that contains a number of $(x, y)$ pairs, where $x$ and $y$ are vectors of same dimension ($K$). My goal is to find a projection matrix so $\phi^*$ of dimension $K ...
0
votes
0answers
30 views

How to find the variance of B1 hat through matrix OLS estimation?

I've been working on this problem to which I have no solution, and I have absolutely not the slightest idea how to solve it. Intuition tells me that I should go for the covariance-variance matrix but ...
2
votes
3answers
179 views

What does that statistically mean , if $(X'X)^{-1}$ does not exist?

It is not a real world case , but suppose that we have $n$ observations and $k$ variables , since $k= n - 1 $ , if $X$ is the design matrix,$(X'X)$ will be a square matrix , so What does that ...
6
votes
1answer
149 views

How is the determinant of (X'X) related to variance?

I'm working on a problem (and actually have the answer) but I don't know why this is the answer, can someone explain this equality?. It has to do with the the determinant of the partitioned matrix ...
1
vote
2answers
56 views

Multiple linear regression problem

I am stuck at this question. For example I have B=(X'X)^-1X'Y but I cannot go further and make He a part of the model. Any suggestions on how to proceed?
1
vote
1answer
38 views

What is the meaning of data represented as matrix in multivariate analysis?

Suppose there are p-variate n observations represented by a matrix $X$ of dim $n$ x $p$. $n$ : No of observations $p$ : No of variables in each observation So if i take the row-vector and draw all ...
1
vote
1answer
27 views

What's special about (x'x-x'Proj(w)x)?

I'm working on my homework and I keep seeing something like $$(x'x-x'W(W'W)^{-1}W'x)$$ I know that $W(W'W)^{-1}W'$ is the projection matrix, but what is so special about subtracting those two inner ...
0
votes
0answers
48 views

Quantifying symmetry across the diagonal in asymmetric dissimilarity matrix

I've got a dissimilarity matrix constructed from pairwise similarity ratings. These similarity ratings are often asymmetrical (i.e., matrix[i,j] != matrix[j,i]), and the differences between the ij and ...
0
votes
1answer
30 views

method for calculating portfolio volatility

I am trying to figure out the method for calculating the portfolio volatility using matrices. I have read online the following definition for calculating the portfolio volatility using matrix algebra ...