updated index pages

The index pages were updated with the recently added proofs/definitions.

Author: JoramSoch

I/DbA.md

@@ -8,7 +8,7 @@ title: "Definition by Author"
 
 - [Sample covariance](/D/cov-samp)
 
-### JoramSoch (169 definitions)
+### JoramSoch (170 definitions)
 
 - [Akaike information criterion](/D/aic)
 - [Alternative hypothesis](/D/h1)
@@ -38,6 +38,7 @@ title: "Definition by Author"
 - [Covariance](/D/cov)
 - [Covariance matrix](/D/covmat)
 - [Critical value](/D/cval)
+- [Cross-covariance matrix](/D/covmat-cross)
 - [Cross-entropy](/D/ent-cross)
 - [Cross-validated log model evidence](/D/cvlme)
 - [Cumulant-generating function](/D/cgf)

I/DbN.md

@@ -182,3 +182,4 @@ title: "Definition by Number"
 | D173 | mse | [Mean squared error](/D/mse) | JoramSoch | 2022-03-27 |
 | D174 | ci | [Confidence interval](/D/ci) | JoramSoch | 2022-03-27 |
 | D175 | nw | [Normal-Wishart distribution](/D/nw) | JoramSoch | 2022-05-14 |
+| D176 | covmat-cross | [Cross-covariance matrix](/D/covmat-cross) | JoramSoch | 2022-09-26 |

I/DbT.md

@@ -42,6 +42,7 @@ title: "Definition by Topic"
 - [Covariance](/D/cov)
 - [Covariance matrix](/D/covmat)
 - [Critical value](/D/cval)
+- [Cross-covariance matrix](/D/covmat-cross)
 - [Cross-entropy](/D/ent-cross)
 - [Cross-validated log model evidence](/D/cvlme)
 - [Cumulant-generating function](/D/cgf)

I/PbA.md

@@ -8,7 +8,7 @@ title: "Proof by Author"
 
 - [Covariance matrix of the multinomial distribution](/P/mult-cov)
 
-### JoramSoch (331 proofs)
+### JoramSoch (336 proofs)
 
 - [Accuracy and complexity for the univariate Gaussian](/P/ug-anc)
 - [Accuracy and complexity for the univariate Gaussian with known variance](/P/ugkv-anc)
@@ -49,6 +49,7 @@ title: "Proof by Author"
 - [Covariance matrix of the categorical distribution](/P/cat-cov)
 - [Covariance matrix of the multivariate normal distribution](/P/mvn-cov)
 - [Covariance of independent random variables](/P/cov-ind)
+- [Covariance of the sum of two random vectors](/P/covmat-sum)
 - [Cross-validated log Bayes factor for the univariate Gaussian with known variance](/P/ugkv-cvlbf)
 - [Cross-validated log model evidence for the univariate Gaussian with known variance](/P/ugkv-cvlme)
 - [Cumulative distribution function in terms of probability density function of a continuous random variable](/P/cdf-pdf)
@@ -219,6 +220,7 @@ title: "Proof by Author"
 - [Partition of the log model evidence into accuracy and complexity](/P/lme-anc)
 - [Partition of the mean squared error into bias and variance](/P/mse-bnv)
 - [Partition of variance into expected values](/P/var-mean)
+- [Positive semi-definiteness of the covariance matrix](/P/covmat-psd)
 - [Posterior credibility region against the omnibus null hypothesis for Bayesian linear regression](/P/blr-pcr)
 - [Posterior density is proportional to joint likelihood](/P/post-jl)
 - [Posterior distribution for Bayesian linear regression](/P/blr-post)
@@ -314,8 +316,11 @@ title: "Proof by Author"
 - [Scaling of the covariance matrix upon multiplication with constant matrix](/P/covmat-scal)
 - [Scaling of the variance upon multiplication with a constant](/P/var-scal)
 - [Second central moment is variance](/P/momcent-2nd)
+- [Self-covariance equals variance](/P/cov-var)
 - [Simple linear regression is a special case of multiple linear regression](/P/slr-mlr)
 - [Sums of squares for simple linear regression](/P/slr-sss)
+- [Symmetry of the covariance](/P/cov-symm)
+- [Symmetry of the covariance matrix](/P/covmat-symm)
 - [t-distribution is a special case of multivariate t-distribution](/P/t-mvt)
 - [The p-value follows a uniform distribution under the null hypothesis](/P/pval-h0)
 - [The regression line goes through the center of mass point](/P/slr-comp)

I/PbN.md

@@ -354,3 +354,8 @@ title: "Proof by Number"
 | P346 | ng-samp | [Sampling from the normal-gamma distribution](/P/ng-samp) | JoramSoch | 2022-09-22 |
 | P347 | covmat-inv | [Invariance of the covariance matrix under addition of constant vector](/P/covmat-inv) | JoramSoch | 2022-09-22 |
 | P348 | covmat-scal | [Scaling of the covariance matrix upon multiplication with constant matrix](/P/covmat-scal) | JoramSoch | 2022-09-22 |
+| P349 | covmat-sum | [Covariance of the sum of two random vectors](/P/covmat-sum) | JoramSoch | 2022-09-26 |
+| P350 | covmat-symm | [Symmetry of the covariance matrix](/P/covmat-symm) | JoramSoch | 2022-09-26 |
+| P351 | covmat-psd | [Positive semi-definiteness of the covariance matrix](/P/covmat-psd) | JoramSoch | 2022-09-26 |
+| P352 | cov-var | [Self-covariance equals variance](/P/cov-var) | JoramSoch | 2022-09-26 |
+| P353 | cov-symm | [Symmetry of the covariance](/P/cov-symm) | JoramSoch | 2022-09-26 |

I/PbT.md

@@ -53,6 +53,7 @@ title: "Proof by Topic"
 - [Covariance matrix of the multinomial distribution](/P/mult-cov)
 - [Covariance matrix of the multivariate normal distribution](/P/mvn-cov)
 - [Covariance of independent random variables](/P/cov-ind)
+- [Covariance of the sum of two random vectors](/P/covmat-sum)
 - [Cross-validated log Bayes factor for the univariate Gaussian with known variance](/P/ugkv-cvlbf)
 - [Cross-validated log model evidence for the univariate Gaussian with known variance](/P/ugkv-cvlme)
 - [Cumulative distribution function in terms of probability density function of a continuous random variable](/P/cdf-pdf)
@@ -267,6 +268,7 @@ title: "Proof by Topic"
 - [Partition of the log model evidence into accuracy and complexity](/P/lme-anc)
 - [Partition of the mean squared error into bias and variance](/P/mse-bnv)
 - [Partition of variance into expected values](/P/var-mean)
+- [Positive semi-definiteness of the covariance matrix](/P/covmat-psd)
 - [Posterior credibility region against the omnibus null hypothesis for Bayesian linear regression](/P/blr-pcr)
 - [Posterior density is proportional to joint likelihood](/P/post-jl)
 - [Posterior distribution for Bayesian linear regression](/P/blr-post)
@@ -376,8 +378,11 @@ title: "Proof by Topic"
 - [Scaling of the covariance matrix upon multiplication with constant matrix](/P/covmat-scal)
 - [Scaling of the variance upon multiplication with a constant](/P/var-scal)
 - [Second central moment is variance](/P/momcent-2nd)
+- [Self-covariance equals variance](/P/cov-var)
 - [Simple linear regression is a special case of multiple linear regression](/P/slr-mlr)
 - [Sums of squares for simple linear regression](/P/slr-sss)
+- [Symmetry of the covariance](/P/cov-symm)
+- [Symmetry of the covariance matrix](/P/covmat-symm)
 
 ### T