Going thru changes

tex/chapters/multivariate.tex

@@ -9,8 +9,8 @@ In order to estimate a multivariate density using KDE or BKDE, a multivariate ke
 Multivariate kernel functions can be constructed in various ways, however, a popular way is given by the product kernel.
 Such a kernel is constructed by combining several univariate kernels into a product, where each kernel is applied in each dimension with a possibly different bandwidth.
 
-Given a multivariate random variable $\bm{X}=(x_1,\dots ,x_d)$ in $d$ dimensions.
-The sample set $\mathcal{X}$ is a $n\times d$ matrix \cite{scott2015}.
+Given a multivariate random variable $\bm{X}=(x_1,\dots ,x_d)^T$ in $d$ dimensions.
+The sample set $\mathcal{X}=(x_{i,j})=(\bm{X}_1, \dots, \bm{X}_n)$ is a $n\times d$ matrix \cite{scott2015}.
 The multivariate KDE $\hat{f}$ which defines the estimate pointwise at $\bm{u}=(u_1, \dots, u_d)^T$ is given as
 \begin{equation}
 \label{eq:mvKDE}