replaced vector notation

JoramSoch · JoramSoch · commit 09498bb823fa · 2025-11-14T17:14:05.000+01:00
The phrase "$n \times 1$" was replaced by "$n$-dimensional" throughout, except in places where it is important to explicitly denote vectors as column vectors, especially in relation with matrices having the same number of rows.
diff --git a/D/cdf-joint.md b/D/cdf-joint.md
@@ -27,7 +27,7 @@ username: "JoramSoch"
 ---
 
 
-**Definition:** Let $X \in \mathbb{R}^n$ be an $n \times 1$ [random vector](/D/rvec). Then, the [joint](/D/dist-joint) [cumulative distribution function](/D/cdf) of $X$ is defined as the [probability](/D/prob) that each entry $X_i$ is smaller than a specific value $x_i$ for $i = 1, \ldots, n$:
+**Definition:** Let $X \in \mathbb{R}^n$ be an $n$-dimensional [random vector](/D/rvec). Then, the [joint](/D/dist-joint) [cumulative distribution function](/D/cdf) of $X$ is defined as the [probability](/D/prob) that each entry $X_i$ is smaller than a specific value $x_i$ for $i = 1, \ldots, n$:
 
 $$ \label{eq:cdf-joint}
 F_X(x) = \mathrm{Pr}(X_1 \leq x_1, \ldots, X_n \leq x_n) \; .
diff --git a/D/mean-rvec.md b/D/mean-rvec.md
@@ -33,7 +33,7 @@ username: "JoramSoch"
 ---
 
 
-**Definition:** Let $X$ be an $n \times 1$ [random vector](/D/rvec). Then, the [expected value](/D/mean) of $X$ is an $n \times 1$ vector whose entries correspond to the expected values of the entries of the random vector:
+**Definition:** Let $X$ be an $n$-dimensional [random vector](/D/rvec). Then, the [expected value](/D/mean) of $X$ is an $n$-dimensional vector whose entries correspond to the expected values of the entries of the random vector:
 
 $$ \label{eq:mean-rvec}
 \mathrm{E}(X) = \mathrm{E}\left( \left[ \begin{array}{c} X_1 \\ \vdots \\ X_n \end{array} \right] \right) = \left[ \begin{array}{c} \mathrm{E}(X_1) \\ \vdots \\ \mathrm{E}(X_n) \end{array} \right] \; .
diff --git a/D/mvn.md b/D/mvn.md
@@ -28,7 +28,7 @@ username: "JoramSoch"
 ---
 
 
-**Definition:** Let $X$ be an $n \times 1$ [random vector](/D/rvec). Then, $X$ is said to be multivariate normally distributed with mean $\mu$ and covariance $\Sigma$
+**Definition:** Let $X$ be an $n$-dimensional [random vector](/D/rvec). Then, $X$ is said to be multivariate normally distributed with mean $\mu$ and covariance $\Sigma$
 
 $$ \label{eq:mvn}
 X \sim \mathcal{N}(\mu, \Sigma) \; ,
@@ -40,4 +40,4 @@ $$ \label{eq:mvn-pdf}
 \mathcal{N}(x; \mu, \Sigma) = \frac{1}{\sqrt{(2 \pi)^n |\Sigma|}} \cdot \exp \left[ -\frac{1}{2} (x-\mu)^\mathrm{T} \Sigma^{-1} (x-\mu) \right]
 $$
 
-where $\mu$ is an $n \times 1$ real vector and $\Sigma$ is an $n \times n$ positive-definite matrix.
+where $\mu$ is an $n$-dimensional real vector and $\Sigma$ is an $n \times n$ positive-definite matrix.
diff --git a/D/mvt.md b/D/mvt.md
@@ -28,7 +28,7 @@ username: "JoramSoch"
 ---
 
 
-**Definition:** Let $X$ be an $n \times 1$ [random vector](/D/rvec). Then, $X$ is said to follow a multivariate $t$-distribution with mean $\mu$, scale matrix $\Sigma$ and degrees of freedom $\nu$
+**Definition:** Let $X$ be an $n$-dimensional [random vector](/D/rvec). Then, $X$ is said to follow a multivariate $t$-distribution with mean $\mu$, scale matrix $\Sigma$ and degrees of freedom $\nu$
 
 $$ \label{eq:mvt}
 X \sim t(\mu, \Sigma, \nu) \; ,
@@ -40,4 +40,4 @@ $$ \label{eq:mvt-pdf}
 t(x; \mu, \Sigma, \nu) = \sqrt{\frac{1}{(\nu \pi)^{n} |\Sigma|}} \, \frac{\Gamma([\nu+n]/2)}{\Gamma(\nu/2)} \, \left[ 1 + \frac{1}{\nu} (x-\mu)^\mathrm{T} \Sigma^{-1} (x-\mu) \right]^{-(\nu+n)/2}
 $$
 
-where $\mu$ is an $n \times 1$ real vector, $\Sigma$ is an $n \times n$ positive-definite matrix and $\nu > 0$.
+where $\mu$ is an $n$-dimensional real vector, $\Sigma$ is an $n \times n$ positive-definite matrix and $\nu > 0$.
diff --git a/D/ng.md b/D/ng.md
@@ -28,7 +28,7 @@ username: "JoramSoch"
 ---
 
 
-**Definition:** Let $X$ be an $n \times 1$ [random vector](/D/rvec) and let $Y$ be a positive [random variable](/D/rvar). Then, $X$ and $Y$ are said to follow a normal-gamma distribution
+**Definition:** Let $X$ be an $n$-dimensional [random vector](/D/rvec) and let $Y$ be a positive [random variable](/D/rvar). Then, $X$ and $Y$ are said to follow a normal-gamma distribution
 
 $$ \label{eq:ng}
 X,Y \sim \mathrm{NG}(\mu, \Lambda, a, b) \; ,
diff --git a/P/anova1-f.md b/P/anova1-f.md
@@ -141,7 +141,7 @@ $$ \label{eq:cochran-p2}
 Q_j \sim \chi^2(r_j), \; j = 1, \ldots, m \; .
 $$
 
-Let $U$ be the $n \times 1$ column vector of all observations
+Let $U$ be the $n$-dimensional column vector of all observations
 
 $$ \label{eq:U}
 U = \left[ \begin{matrix} u_1 \\ \vdots \\ u_k \end{matrix} \right]
diff --git a/P/anova2-cochran.md b/P/anova2-cochran.md
@@ -190,7 +190,7 @@ $$ \label{eq:cochran-p2}
 Q_j \sim \chi^2(r_j), \; j = 1, \ldots, m \; .
 $$
 
-First, we define the $n \times 1$ vector $U$:
+First, we define the $n$-dimensional vector $U$:
 
 $$ \label{eq:U}
 U = \left[ \begin{matrix} u_{1 \bullet} \\ \vdots \\ u_{a \bullet} \end{matrix} \right] \quad \text{where} \quad u_{i \bullet} = \left[ \begin{matrix} u_{i1} \\ \vdots \\ u_{ib} \end{matrix} \right] \quad \text{where} \quad u_{ij} = \left[ \begin{matrix} (y_{i,j,1} - \mu - \alpha_i - \beta_j - \gamma_{ij})/\sigma \\ \vdots \\ (y_{i,j,n_{ij}} - \mu - \alpha_i - \beta_j - \gamma_{ij})/\sigma \end{matrix} \right] \; .
diff --git a/P/blr-anc.md b/P/blr-anc.md
@@ -47,7 +47,7 @@ $$ \label{eq:GLM}
 m: \; y = X \beta + \varepsilon, \; \varepsilon \sim \mathcal{N}(0, \sigma^2 V)
 $$
 
-be a [linear regression model](/D/mlr) with measured $n \times 1$ data vector $y$, known $n \times p$ design matrix $X$, known $n \times n$ covariance structure $V$ as well as unknown $p \times 1$ regression coefficients $\beta$ and unknown noise variance $\sigma^2$. Moreover, assume a [normal-gamma prior distribution](/P/blr-prior) over the model parameters $\beta$ and $\tau = 1/\sigma^2$:
+be a [linear regression model](/D/mlr) with measured $n$-dimensional data vector $y$, known $n \times p$ design matrix $X$, known $n \times n$ covariance structure $V$ as well as unknown $p \times 1$ regression coefficients $\beta$ and unknown noise variance $\sigma^2$. Moreover, assume a [normal-gamma prior distribution](/P/blr-prior) over the model parameters $\beta$ and $\tau = 1/\sigma^2$:
 
 $$ \label{eq:GLM-NG-prior}
 p(\beta,\tau) = \mathcal{N}(\beta; \mu_0, (\tau \Lambda_0)^{-1}) \cdot \mathrm{Gam}(\tau; a_0, b_0) \; .
diff --git a/P/blr-lbf.md b/P/blr-lbf.md
@@ -21,7 +21,7 @@ username: "JoramSoch"
 ---
 
 
-**Theorem:** Let $y = \left[ y_1, \ldots, y_n \right]^\mathrm{T}$ be an $n \times 1$ vector of a [measured univariate signal](/D/data) and consider two [linear regression models](/D/mlr) with [design matrices](/D/mlr) $X_1, X_2$ and [precision matrices](/P/blr-prior) $P_1, P_2$, entailing potentially different [regression coefficients](/D/mlr) $\beta_1, \beta_2$ and [noise precisions](/P/blr-prior) $\tau_1, \tau_2$:
+**Theorem:** Let $y = \left[ y_1, \ldots, y_n \right]^\mathrm{T}$ be an $n$-dimensional vector of a [measured univariate signal](/D/data) and consider two [linear regression models](/D/mlr) with [design matrices](/D/mlr) $X_1, X_2$ and [precision matrices](/P/blr-prior) $P_1, P_2$, entailing potentially different [regression coefficients](/D/mlr) $\beta_1, \beta_2$ and [noise precisions](/P/blr-prior) $\tau_1, \tau_2$:
 
 $$ \label{eq:GLM-NG-12}
 \begin{split}
diff --git a/P/blr-lme.md b/P/blr-lme.md
@@ -33,7 +33,7 @@ $$ \label{eq:GLM}
 m: \; y = X \beta + \varepsilon, \; \varepsilon \sim \mathcal{N}(0, \sigma^2 V)
 $$
 
-be a [linear regression model](/D/mlr) with measured $n \times 1$ data vector $y$, known $n \times p$ design matrix $X$, known $n \times n$ covariance structure $V$ as well as unknown $p \times 1$ regression coefficients $\beta$ and unknown noise variance $\sigma^2$. Moreover, assume a [normal-gamma prior distribution](/P/blr-prior) over the model parameters $\beta$ and $\tau = 1/\sigma^2$:
+be a [linear regression model](/D/mlr) with measured $n$-dimensional data vector $y$, known $n \times p$ design matrix $X$, known $n \times n$ covariance structure $V$ as well as unknown $p \times 1$ regression coefficients $\beta$ and unknown noise variance $\sigma^2$. Moreover, assume a [normal-gamma prior distribution](/P/blr-prior) over the model parameters $\beta$ and $\tau = 1/\sigma^2$:
 
 $$ \label{eq:GLM-NG-prior}
 p(\beta,\tau) = \mathcal{N}(\beta; \mu_0, (\tau \Lambda_0)^{-1}) \cdot \mathrm{Gam}(\tau; a_0, b_0) \; .
diff --git a/P/blr-post.md b/P/blr-post.md
@@ -33,7 +33,7 @@ $$ \label{eq:GLM}
 y = X \beta + \varepsilon, \; \varepsilon \sim \mathcal{N}(0, \sigma^2 V)
 $$
 
-be a [linear regression model](/D/mlr) with measured $n \times 1$ data vector $y$, known $n \times p$ design matrix $X$, known $n \times n$ covariance structure $V$ as well as unknown $p \times 1$ regression coefficients $\beta$ and unknown noise variance $\sigma^2$. Moreover, assume a [normal-gamma prior distribution](/P/blr-prior) over the model parameters $\beta$ and $\tau = 1/\sigma^2$:
+be a [linear regression model](/D/mlr) with measured $n$-dimensional data vector $y$, known $n \times p$ design matrix $X$, known $n \times n$ covariance structure $V$ as well as unknown $p \times 1$ regression coefficients $\beta$ and unknown noise variance $\sigma^2$. Moreover, assume a [normal-gamma prior distribution](/P/blr-prior) over the model parameters $\beta$ and $\tau = 1/\sigma^2$:
 
 $$ \label{eq:GLM-NG-prior}
 p(\beta,\tau) = \mathcal{N}(\beta; \mu_0, (\tau \Lambda_0)^{-1}) \cdot \mathrm{Gam}(\tau; a_0, b_0) \; .
diff --git a/P/blr-prior.md b/P/blr-prior.md
@@ -33,7 +33,7 @@ $$ \label{eq:GLM}
 y = X \beta + \varepsilon, \; \varepsilon \sim \mathcal{N}(0, \sigma^2 V)
 $$
 
-be a [linear regression model](/D/mlr) with measured $n \times 1$ data vector $y$, known $n \times p$ design matrix $X$, known $n \times n$ covariance structure $V$ as well as unknown $p \times 1$ regression coefficients $\beta$ and unknown noise variance $\sigma^2$.
+be a [linear regression model](/D/mlr) with measured $n$-dimensional data vector $y$, known $n \times p$ design matrix $X$, known $n \times n$ covariance structure $V$ as well as unknown $p \times 1$ regression coefficients $\beta$ and unknown noise variance $\sigma^2$.
 
 Then, the [conjugate prior](/D/prior-conj) for this model is a [normal-gamma distribution](/D/ng)
 
diff --git a/P/blrkc-anc.md b/P/blrkc-anc.md
@@ -40,7 +40,7 @@ $$ \label{eq:GLM}
 m: y = X \beta + \varepsilon, \; \varepsilon \sim \mathcal{N}(0, \Sigma)
 $$
 
-be a [linear regression model](/D/mlr) with measured $n \times 1$ data vector $y$, known $n \times p$ design matrix $X$ and known $n \times n$ covariance matrix $\Sigma$ as well as unknown $p \times 1$ regression coefficients $\beta$. Moreover, assume a [multivariate normal distribution](/P/blrkc-prior) over the model parameter $\beta$:
+be a [linear regression model](/D/mlr) with measured $n$-dimensional data vector $y$, known $n \times p$ design matrix $X$ and known $n \times n$ covariance matrix $\Sigma$ as well as unknown $p \times 1$ regression coefficients $\beta$. Moreover, assume a [multivariate normal distribution](/P/blrkc-prior) over the model parameter $\beta$:
 
 $$ \label{eq:GLM-N-prior}
 p(\beta) = \mathcal{N}(\beta; \mu_0, \Sigma_0) \; .
diff --git a/P/blrkc-lme.md b/P/blrkc-lme.md
@@ -40,7 +40,7 @@ $$ \label{eq:GLM}
 m: y = X \beta + \varepsilon, \; \varepsilon \sim \mathcal{N}(0, \Sigma)
 $$
 
-be a [linear regression model](/D/mlr) with measured $n \times 1$ data vector $y$, known $n \times p$ design matrix $X$ and known $n \times n$ covariance matrix $\Sigma$ as well as unknown $p \times 1$ regression coefficients $\beta$. Moreover, assume a [multivariate normal distribution](/P/blrkc-prior) over the model parameter $\beta$:
+be a [linear regression model](/D/mlr) with measured $n$-dimensional data vector $y$, known $n \times p$ design matrix $X$ and known $n \times n$ covariance matrix $\Sigma$ as well as unknown $p \times 1$ regression coefficients $\beta$. Moreover, assume a [multivariate normal distribution](/P/blrkc-prior) over the model parameter $\beta$:
 
 $$ \label{eq:GLM-N-prior}
 p(\beta) = \mathcal{N}(\beta; \mu_0, \Sigma_0) \; .
diff --git a/P/blrkc-post.md b/P/blrkc-post.md
@@ -40,7 +40,7 @@ $$ \label{eq:GLM}
 y = X \beta + \varepsilon, \; \varepsilon \sim \mathcal{N}(0, \Sigma)
 $$
 
-be a [linear regression model](/D/mlr) with measured $n \times 1$ data vector $y$, known $n \times p$ design matrix $X$ and known $n \times n$ covariance matrix $\Sigma$ as well as unknown $p \times 1$ regression coefficients $\beta$. Moreover, assume a [multivariate normal distribution](/P/blrkc-prior) over the model parameter $\beta$:
+be a [linear regression model](/D/mlr) with measured $n$-dimensional data vector $y$, known $n \times p$ design matrix $X$ and known $n \times n$ covariance matrix $\Sigma$ as well as unknown $p \times 1$ regression coefficients $\beta$. Moreover, assume a [multivariate normal distribution](/P/blrkc-prior) over the model parameter $\beta$:
 
 $$ \label{eq:GLM-N-prior}
 p(\beta) = \mathcal{N}(\beta; \mu_0, \Sigma_0) \; .
diff --git a/P/blrkc-prior.md b/P/blrkc-prior.md
@@ -40,7 +40,7 @@ $$ \label{eq:GLM}
 y = X \beta + \varepsilon, \; \varepsilon \sim \mathcal{N}(0, \Sigma)
 $$
 
-be a [linear regression model](/D/mlr) with measured $n \times 1$ data vector $y$, known $n \times p$ design matrix $X$ and known $n \times n$ covariance matrix $\Sigma$ as well as unknown $p \times 1$ regression coefficients $\beta$.
+be a [linear regression model](/D/mlr) with measured $n$-dimensional data vector $y$, known $n \times p$ design matrix $X$ and known $n \times n$ covariance matrix $\Sigma$ as well as unknown $p \times 1$ regression coefficients $\beta$.
 
 Then, the [conjugate prior](/D/prior-conj) for this model is a [multivariate normal distribution](/D/mvn)
 
diff --git a/P/bvn-pdf.md b/P/bvn-pdf.md
@@ -34,7 +34,7 @@ f_X(x) = \frac{1}{2 \pi \sqrt{\sigma_1^2 \sigma_2^2 - \sigma_{12}^2}} \cdot \exp
 $$
 
 
-**Proof:** The [probability density function of the multivariate normal distribution](/P/mvn-pdf) for an $n \times 1$ [random vector](/D/rvec) $x$ is:
+**Proof:** The [probability density function of the multivariate normal distribution](/P/mvn-pdf) for an $n$-dimensional [random vector](/D/rvec) $x$ is:
 
 $$ \label{eq:mvn-pdf}
 f_X(x) = \frac{1}{\sqrt{(2 \pi)^n |\Sigma|}} \cdot \exp \left[ -\frac{1}{2} (x-\mu)^\mathrm{T} \Sigma^{-1} (x-\mu) \right] \; .
diff --git a/P/bvn-pdfcorr.md b/P/bvn-pdfcorr.md
@@ -78,7 +78,7 @@ $$ \label{eq:Sigma-inv}
 \end{split}
 $$
 
-The [probability density function of the multivariate normal distribution](/P/mvn-pdf) for an $n \times 1$ [random vector](/D/rvec) $x$ is:
+The [probability density function of the multivariate normal distribution](/P/mvn-pdf) for an $n$-dimensional [random vector](/D/rvec) $x$ is:
 
 $$ \label{eq:mvn-pdf}
 f_X(x) = \frac{1}{\sqrt{(2 \pi)^n |\Sigma|}} \cdot \exp \left[ -\frac{1}{2} (x-\mu)^\mathrm{T} \Sigma^{-1} (x-\mu) \right] \; .
diff --git a/P/matn-dent.md b/P/matn-dent.md
@@ -46,7 +46,7 @@ $$ \label{eq:mvn-dent}
 X \sim \mathcal{N}(\mu, \Sigma) \quad \Rightarrow \quad \mathrm{h}(X) = \frac{n}{2} \ln(2\pi) + \frac{1}{2} \ln|\Sigma| + \frac{1}{2} n
 $$
 
-where $X$ is an $n \times 1$ [random vector](/D/rvec). Thus, we can plug the distribution parameters from \eqref{eq:matn} into the differential entropy in \eqref{eq:mvn-dent} using the relationship given by \eqref{eq:matn-mvn}:
+where $X$ is an $n$-dimensional [random vector](/D/rvec). Thus, we can plug the distribution parameters from \eqref{eq:matn} into the differential entropy in \eqref{eq:mvn-dent} using the relationship given by \eqref{eq:matn-mvn}:
 
 $$ \label{eq:matn-dent-s1}
 \mathrm{h}(X) = \frac{np}{2} \ln(2\pi) + \frac{1}{2} \ln|V \otimes U| + \frac{1}{2} np \; .
diff --git a/P/matn-kl.md b/P/matn-kl.md
@@ -52,7 +52,7 @@ $$ \label{eq:mvn-KL}
 \mathrm{KL}[P\,||\,Q] = \frac{1}{2} \left[ (\mu_2 - \mu_1)^T \Sigma_2^{-1} (\mu_2 - \mu_1) + \mathrm{tr}(\Sigma_2^{-1} \Sigma_1) - \ln \frac{|\Sigma_1|}{|\Sigma_2|} - n \right]
 $$
 
-where $X$ is an $n \times 1$ [random vector](/D/rvec).
+where $X$ is an $n$-dimensional [random vector](/D/rvec).
 
 Thus, we can plug the distribution parameters from \eqref{eq:matns} into the KL divergence in \eqref{eq:mvn-KL} using the relationship given by \eqref{eq:matn-mvn}
 
diff --git a/P/mean-qf.md b/P/mean-qf.md
@@ -44,7 +44,7 @@ username: "JoramSoch"
 ---
 
 
-**Theorem:** Let $X$ be an $n \times 1$ [random vector](/D/rvec) with [mean](/D/mean) $\mu$ and [covariance](/D/covmat) $\Sigma$ and let $A$ be a symmetric $n \times n$ matrix. Then, the expectation of the quadratic form $X^\mathrm{T} A X$ is
+**Theorem:** Let $X$ be an $n$-dimensional [random vector](/D/rvec) with [mean](/D/mean) $\mu$ and [covariance](/D/covmat) $\Sigma$ and let $A$ be a symmetric $n \times n$ matrix. Then, the expectation of the quadratic form $X^\mathrm{T} A X$ is
 
 $$ \label{eq:mean-qf}
 \mathrm{E}\left[ X^\mathrm{T} A X \right] = \mu^\mathrm{T} A \mu + \mathrm{tr}(A \Sigma) \; .
diff --git a/P/mgf-ltt.md b/P/mgf-ltt.md
@@ -27,7 +27,7 @@ username: "JoramSoch"
 ---
 
 
-**Theorem:** Let $X$ be an $n \times 1$ [random vector](/D/rvec) with the [moment-generating function](/D/mgf) $M_X(t)$. Then, the moment-generating function of the linear transformation $Y = A X + b$ is given by
+**Theorem:** Let $X$ be an $n$-dimensional [random vector](/D/rvec) with the [moment-generating function](/D/mgf) $M_X(t)$. Then, the moment-generating function of the linear transformation $Y = A X + b$ is given by
 
 $$ \label{eq:mgf-ltt}
 M_Y(t) = \exp \left[ t^\mathrm{T} b \right] \cdot M_X(At)
diff --git a/P/mlr-glm.md b/P/mlr-glm.md
@@ -42,7 +42,7 @@ $$ \label{eq:mlr}
 y = X\beta + \varepsilon, \; \varepsilon \sim \mathcal{N}(0, \sigma^2 V) \; .
 $$
 
-Because $\varepsilon$ is an $n \times 1$ vector and $\sigma^2$ is scalar, we have the following identities:
+Because $\varepsilon$ is an $n$-dimensional vector and $\sigma^2$ is scalar, we have the following identities:
 
 $$
 \begin{split}
diff --git a/P/mlr-llr.md b/P/mlr-llr.md
@@ -27,7 +27,7 @@ username: "JoramSoch"
 ---
 
 
-**Theorem:** Let $y = \left[ y_1, \ldots, y_n \right]^\mathrm{T}$ be an $n \times 1$ [data vector](/D/data) and consider a [linear regression model](/D/mlr) $m_1$ with [design matrix](/D/mlr) $X = \left[ X_0, X_1 \right] \in \mathbb{R}^{n \times p}$ as well as a reduced [linear regression model](/D/mlr) $m_0$ with [design matrix](/D/mlr) $X_0 \in \mathbb{R}^{n \times p_0}$:
+**Theorem:** Let $y = \left[ y_1, \ldots, y_n \right]^\mathrm{T}$ be an $n$-dimensional [data vector](/D/data) and consider a [linear regression model](/D/mlr) $m_1$ with [design matrix](/D/mlr) $X = \left[ X_0, X_1 \right] \in \mathbb{R}^{n \times p}$ as well as a reduced [linear regression model](/D/mlr) $m_0$ with [design matrix](/D/mlr) $X_0 \in \mathbb{R}^{n \times p_0}$:
 
 $$ \label{eq:m1-m0}
 \begin{split}
diff --git a/P/mlr-rssdist.md b/P/mlr-rssdist.md
@@ -85,7 +85,7 @@ $$ \label{eq:y-tilde-dist}
 \tilde{y} \sim \mathcal{N}(\tilde{X} \beta, \sigma^2 I_n) \; .
 $$
 
-With that, we have obtained a [linear regression model](/D/mlr) with independent observations. [Cochran's theorem for multivariate normal variables](/P/mvn-cochran) states that, for an $n \times 1$ [normal random vector](/D/mvn) whose [covariance matrix](/D/covmat) is a scalar multiple of the identity matrix, a specific squared form will follow a [non-central chi-squared distribution](/D/ncchi2) where the degrees of freedom and the non-centrality paramter depend on the matrix in the quadratic form:
+With that, we have obtained a [linear regression model](/D/mlr) with independent observations. [Cochran's theorem for multivariate normal variables](/P/mvn-cochran) states that, for an $n$-dimensional [normal random vector](/D/mvn) whose [covariance matrix](/D/covmat) is a scalar multiple of the identity matrix, a specific squared form will follow a [non-central chi-squared distribution](/D/ncchi2) where the degrees of freedom and the non-centrality paramter depend on the matrix in the quadratic form:
 
 $$ \label{eq:mvn-cochran}
 x \sim \mathcal{N}(\mu, \sigma^2 I_n) \quad \Rightarrow \quad y = x^\mathrm{T} A x /\sigma^2 \sim \chi^2\left( \mathrm{rk}(A), \mu^\mathrm{T} A \mu \right) \; .
diff --git a/P/mlr-tsingle.md b/P/mlr-tsingle.md
@@ -48,7 +48,7 @@ $$ \label{eq:mlr-t-single}
 t_j = \frac{\hat{\beta}_j}{\sqrt{\left( \hat{\varepsilon}^\mathrm{T} V^{-1} \hat{\varepsilon} \right)/(n-p) \; \sigma_{jj}}}
 $$
 
-with the $n \times 1$ [vector of residuals](/P/mlr-mat)
+with the $n$-dimensional [vector of residuals](/P/mlr-mat)
 
 $$ \label{eq:mlr-eps-est}
 \hat{\varepsilon} = y - X\hat{\beta}
diff --git a/P/mvn-chi2.md b/P/mvn-chi2.md
@@ -28,7 +28,7 @@ username: "JoramSoch"
 ---
 
 
-**Theorem:** Let $x$ be an $n \times 1$ [random vector](/D/rvec) following a [multivariate normal distribution](/D/mvn) with [zero mean](/D/mean-rvec) and arbitrary [covariance matrix](/P/mvn-cov) $\Sigma$:
+**Theorem:** Let $x$ be an $n$-dimensional [random vector](/D/rvec) following a [multivariate normal distribution](/D/mvn) with [zero mean](/D/mean-rvec) and arbitrary [covariance matrix](/P/mvn-cov) $\Sigma$:
 
 $$ \label{eq:mvn}
 x \sim \mathcal{N}(0, \Sigma) \; .
diff --git a/P/mvn-ind.md b/P/mvn-ind.md
diff --git a/P/mvn-indprod.md b/P/mvn-indprod.md
diff --git a/P/mvn-kl.md b/P/mvn-kl.md
diff --git a/P/mvt-f.md b/P/mvt-f.md
diff --git a/P/ng-dent.md b/P/ng-dent.md
diff --git a/P/ng-kl.md b/P/ng-kl.md
diff --git a/P/norm-lincomb.md b/P/norm-lincomb.md
diff --git a/P/nst-t.md b/P/nst-t.md
diff --git a/P/pdf-invfct.md b/P/pdf-invfct.md
diff --git a/P/pdf-linfct.md b/P/pdf-linfct.md
diff --git a/P/pmf-invfct.md b/P/pmf-invfct.md
