1
vote
2answers
47 views

The inverse of AR structure correlation matrix / Kac-Murdock-Szeg ╠ło matrix

I want to find the inverse of the following matrix: $$ R_{k-1}=\begin{pmatrix} 1 &\rho &\rho^2 &\cdots &\rho^{k-2} \\ \rho &1 &\rho &\cdots ...
0
votes
0answers
5 views

Matrix with highly correlated adjacency entries

I am learning about SVD from this book. One of the exercise questions asks me to create matrix with highly correlated adjacency entries and then conduct some experiments to discover the nature of the ...
0
votes
0answers
17 views

Checking hand manipulations of matrices

Beginning with a 4*3 matrix: 5 4 -1 2 3 -3 3 4 -4 1 3 -2 I have to perform four manipulations on it, which I did by hand. I wanted to ask if my thinking and/or ...
0
votes
0answers
17 views

Exponentially weighted rank ordered correlation matrix

Is there any well-known method to apply exponential weighting (similar to EWMA) to rank ordered correlation matrices such as Kendall tau or Spearman?
0
votes
0answers
15 views

similarities between two binary matrices

I want to measure the similarities between two matrices A and B. Both A and B contains the feature vectors of sounds and are in binary format. i want to see what is the similarities between these two ...
0
votes
0answers
25 views

Correlating random numbers seems to skew the data

I am trying to generate a series of correlated random numbers that represent currency exchange rates for a Monte-Carlo simulation. I am attempting to do this via a Cholesky decomposition of the ...
0
votes
0answers
28 views

Condition number of covariance matrix

I am interested in generating a covariance matrix of dimension say 100. I managed to get a correlation matrix with finite condition number. To construct a covariance matrix I need to have standard ...
0
votes
0answers
8 views

How to order a set of attributes such that their correlation matrix concentrates high correlation terms around the diagonal?

Suppose there are n attributes that are being tested for correlation with one another. We need to find the order in which these attributes must be placed along the rows as well as columns such that ...
0
votes
1answer
195 views

How to construct a covariance matrix from a 2x2 data set

so if given a covariance matrix I can find the eigenvalues and move forward from there... but I seem to have trouble with the step before if I am given a data set and am told to create the covariance ...
1
vote
0answers
49 views

Redundancies in covariance matrix

We know that covariance matrix is symmetrical. I have a vague intuition that there may be some other redundancies beyond that. For example, if A is correlated to B and B is correlated to C then A and ...
1
vote
3answers
807 views

Determinant of a N symmetric square matrix with diagonal 1

What is the determinant of a symmetric $n \times n$ matrix with all diagonals be 1 and all others are $\rho$ (yes correlation matrix)? Anyone can tell me a method to work it out elegantly? Thanks!
5
votes
2answers
640 views

Eigenvalue decomposition of block covariance matrix for Canonical Correlation Analysis (CCA)

Edited: My question is related to a tutorial I was reading. The covariance matrix is a block matrix where $C_{xx}$ and $C_{yy}$ are within-set covariance matrices and $C_{xy} = C_{yx}^T$ are ...
2
votes
1answer
546 views

Calculate a whitening matrix without using inverses?

Consider a random column vector $\mathbf{x}$, of dimension $m$. That is, it is a random vector, composed of $m$ random variables. The PDF of the random vector $\mathbf{x}$ is thus the joint-PDF of its ...
3
votes
1answer
429 views

Necessary and sufficient conditions for a matrix to be a valid correlation matrix.

It's not too hard to see that any correlation matrix must have certain properties, such as all entries in the range -1 to 1, symmetric, positive semi-definite (excluding pathological cases like ...
0
votes
1answer
105 views

Find 3 normal variables which are linear combinations based on 3 ind std normal variable given a correlation matrix

I am given $3$ normal random variables $X_1$,$X_2$,$X_3$ which are linear combinations of $Z_1$,$Z_2$,$Z_3$. $Z_1$,$Z_2$,$Z_3$ are mutually independent standard normal variables. I am given a ...
0
votes
1answer
258 views

Calculate Upper Lower bound in $4\times 4$ correlation matrix

Let $X_i$, $i = 1,2,3 4$, be random variables on the same probability space such that $$\begin{align*} \mathrm{corr}(X_1,X_3) &= 0.3;\\ \mathrm{corr}(X_2,X_3) &= 0.1;\\ ...
2
votes
1answer
1k views

Generalized variance

Generalized variance is the determinant of correlation matrix. Does increasing the off-diagonal entries (correlation coefficients) decreases the determinant? Is a proof available? All elements are ...
4
votes
3answers
849 views

Bounds on off-diagonal entries of a correlation matrix

Assume that all the entries of an $n \times n$ correlation matrix which are not on the main diagonal are equal to $q$. Find upper and lower bounds on the possible values of $q$. I know that the ...
2
votes
2answers
899 views

How to 'minimize' correlation between series

Hi fellow mathemagicians, let's say that I have 3 series of numerical results (they represent 'drawdowns') : ...
6
votes
4answers
877 views

Going back from a correlation matrix to the original matrix

I have N sensors which are been sampled M times, so I have an N by M readout matrix. If I want to know the relation and dependencies of these sensors simplest thing is to do a Pearson's correlation ...