Issues-with-covaraince-matrix.md

-The covaraince matrix is a crucial input in our analysis. In our analysis, we estimated the covaraiance matric from several off-source samples.
-We use the invesre of the covaraince matrix to compute the weigted inner product between two vectors, such as inner product between two templates or between template and on-source Y(\alpha). So, the accurate computatation of the inverse matrix is essential for getting the robust results. One can check this accuracy using the following property, the inverse of a matrix is such that if it is multiplied by the original matrix, it results in identity matrix.
+The covariance matrix ( $`\Sigma`$ ) is a crucial input in our analysis. In our analysis, we estimated the covariance matric from several off-source samples.
+We use the inverse of the covariance matrix to compute the weighted inner product between two vectors, such as inner product between two templates or between the template $`S(\alpha)`$ and on-source $`Y(\alpha)`$. So, the accurate computation of the inverse matrix is essential for getting robust results. One can check this accuracy using the following property; the inverse of a matrix is such that if it is multiplied by the original matrix, it results in the identity matrix.
+```math
+\Sigma^{-1} \: \Sigma =  \Sigma \: \Sigma^{-1} = I
+```
+