Search Results

I tried to write a simple function to decompose the lower triangular matrix $L$. I know there is a C++ function of GSL/gsl_linalg_cholesky_ decomp that can do it. …

is a lower triangular matrix. … If the above holds true, suppose an $N\times p$ matrix $X$ generated according to $N(0,I_{p\times p})$ and is then set as fixed. …

We know that a matrix is irreducible if it is not similar via a permutation to a block upper triangular matrix. Is the transition matrix of a irreducible Markov chain irreducible? …

It seems that it is more natural to represent a covariance matrix by it's lower triangular Cholesky factorization. … What are the uses of the upper triangular part? …

The question is: Suppose I randomly (say standard normal distribution) generate a $N \times N$ symmetric matrix, (for example, I generate upper triangular matrix, and fill the bottom half to make sure … it is symmetric), what is the chance it is a positive definite matrix? …

I would realize this: draw length($\beta_s$) independent $\mathcal N(0,1)$ values to create a random vector $z$, then $\beta^*$=$\hat{\beta}+Az$ where $A$ is the upper triangular matrix of the Cholesky … decomposition matrix ($\hat{V}=A'A$). …

In my model it is recommended to have W as a lower triangular Matrix....Any idea about the appropriate way to handle this issue providing R code for the reference Build.dlm.corr.dns =function(param) … #correlated factors { G= matrix(param[1:9],3,3) #3X3 matrix I= diag(3) zero= diag(10^1-10,3,3) G= rbind(cbind(G,I-G),cbind(zero,I)) #16 X3 matrix W1= matrix(c(param[10],0,0,param[11],param …

matrix with elements value $-\infty$ . … However, we could achieve the same with a multiplicative mask with the output of softmax as follows, $$\alpha = Softmax(QK^T)*LTMask$$ where $LTMask$ is the Lower triangular matrix with elements value …

Hence $\hat{\beta} z = \hat{\beta} \Gamma^{-1} x$ where $\Gamma^{-1}$ is a lower triangular matrix. … Hence the regression of $y$ on $x_i$ $\sum\limits_{i=p}^{n} \eta\hat{\beta}_i$. where $\eta$ is obtained by inverting $\Gamma$ and the fact the inverse of an upper triangular matrix is a lower triangular …

Let $\Sigma$ be a positive-definite matrix whose diagonal entries are identically 1. (i.e. $\Sigma$ is a correlation matrix.) … If $L$ is an lower-triangular matrix such that $L^T L = \Sigma$, can the entries of $L$ be bounded? (i.e. do there exist real numbers $l, u$ such that $l \geq (L)_{ij} \leq u$?) …

This generated a triangular matrix (M1) where the diagonal is 1 because A1 = A1, A2 = A2, etc. All other comparisons are between 0 (no similarity) and 1 (identical). … I then did the same thing for protein B, comparing the 5 protein B homologs (B1..B5) to generate a second triangular matrix (M2). …

I have a process described as $r_t = \mu + \Sigma_t^{1/2}z_t$ where $z_t$ is let's say a standard normal distribution residual and $\Sigma_t$ is the conditional covariance matrix. … So my question is whether the matrix $\alpha_{i,j,t}$ is the upper triangular matrix as obtained by f.e. the chol(x) function in Matlab or does it stand for something else? …

I understand it as as the square root of the covariance matrix being the multivariate generalization of taking the sqrt of the variance and then transforming a standard normal variable. … $\mathbf{L}$ is a lower triangular matrix, so when I sample a GP with a vector of standard normal variables (like this https://katbailey.github.io/post/gaussian-processes-for-dummies/), the first output …

We can take a covariance matrix $\Sigma$ and decompose this into a lower and upper triangular matrix $\Sigma = U^T U$ where $U$ is the Cholesky matrix. … decomposition of $\Sigma^{-1} = L^T L$, the procedure that the authors have used to enforce this dependency is simply to take the two standard normal variables $X$ and $Y$ and multiply them by the lower triangular …

$C=L \cdot L^*$, where $L$ is a lower triangular matrix. So I basically populate the diagonal and the lower triangular part of $L$ with my random numbers and compute $C$. … $\mathrm{corr}$ is the correlation matrix and $\mathrm{diag}(\Sigma)$ is a diagonal matrix holding the variances (see also Wikipedia article on covariance matrix). …