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 Jul3 comment Generating correlated random numbers: Why does Cholesky decomposition work? But how do you specify whether the correlations of those variables are going to be positive or negative? Jul1 asked Where does the “2” come from in deriving Normal PDF from its kernel? Nov5 asked Numeric synaesthesia: uses of and advice for learning math. Oct4 awarded Supporter Feb16 awarded Editor Feb16 revised So is this, finally, the difference between convergence in probability and almost sure convergence? Updated to candidate definitions that don't contradict convergence almost surely implying convergence in probability. Feb16 comment So is this, finally, the difference between convergence in probability and almost sure convergence? You're right. How about: only the third statement (A_n/B_n -> 0) needs to be true for convergence in probability, while the first and third statements both need to be true for convergence almost surely? Feb16 asked So is this, finally, the difference between convergence in probability and almost sure convergence? Jun18 comment Reconciling 'intersecting planes' and 'linear transformation' interpretations of matrices According to Wolfram Mathworld... "The dot product therefore has the geometric interpretation as the length of the projection of X onto the unit vector $\bf \hat Y$ when the two vectors are placed so that their tails coincide.". Now I'm confused-- it's not a projection of $\bf X$ onto $\bf Y$ but it is onto its unit vector? Jun18 comment Reconciling 'intersecting planes' and 'linear transformation' interpretations of matrices I was going by this post. Perhaps I'm not interpreting what the author said about the dot product being the part of one vector that's in the direction of the other vector? Jun16 comment Reconciling 'intersecting planes' and 'linear transformation' interpretations of matrices @mac: dot prodcut of x with itself is magnitude of $x$ times cos(0) times the magnitude of the other vector $\in R^1$ which happens to also be $x$. So, 10x1x10. So it seems like the dot product collapses neatly into ordinary scalar multiplication in the degenerate case. Regarding the second comment, I forgot to mention that for my purposes I'm assuming all normal vectors to be through the origin. Jun16 revised Reconciling 'intersecting planes' and 'linear transformation' interpretations of matrices edited tags Jun16 awarded Student Jun16 asked Reconciling 'intersecting planes' and 'linear transformation' interpretations of matrices