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 Jun 30 comment Cholesky decomposition and variance It actually may be better to write it as just $Cov(A+BZ)=B^TCov(Z)B$, since of course adding a constant has no effect on variance and so $Cov(A)=0$, a reference can be found here: en.wikipedia.org/wiki/…. Jun 30 comment Cholesky decomposition and variance $Cov(A + BZ) = Cov(A) + B^TCov(Z)B$. This is a direct result of the linearity of expectation. However it should be clear right away that it definitely can't be just $B$, since the covariance matrix must be positive semi-definite. Jun 30 answered How do you determine the end behavior of a rational function? Jun 30 comment When trying to learn analysis from bottom up, what numbers should I first construct? mathematicians aren't interested in foundations Jun 24 revised Matrix Dimension's effect on Positive Definiteness added 39 characters in body Jun 24 answered Matrix Dimension's effect on Positive Definiteness Jun 23 comment Default positive/(non-negative) probability distribution It appears to be a generalization of the exponential distribution for the specification of higher moments. There is no 'equivalent' distribution in the absolute sense, it appears to be equivalent in the sense of maximizing entropy. Whether or not maximizing entropy is the right call for capturing your lack of prior knowledge in the model is entirely up to your own judgement of the problem. Jun 23 comment Default positive/(non-negative) probability distribution Note that assuming a normal distribution also requires estimates for the mean and variance. I'm sure there is info online on the average volume of oxygen inhaled per minute/hour whatever. Jun 23 comment Default positive/(non-negative) probability distribution If you have some data to calculate the sample mean and sample variance, then you might take a look at this answer: stats.stackexchange.com/questions/83069/…. For a given mean and variance, the normal distribution maximizes entropy, this answer appears to provide the equivalent for a distribution with strictly nonnegative support. Jun 23 comment What math preparation is needed before reading the mathematical method in financial markets? measure theoretic probability, stochastic calculus, stochastic differential equations, looking at the table of contents that book is no joke. Even if you knew all that stuff I wouldn't recommend that book for a first pass. Jun 22 comment Does there exist a function $F(x)$, so that $F'(x)$ is not Riemann integrable? man wtf, are these objects just anomalies of the real line, why would the universe allow such abominations to exist? Jun 22 revised How much information does learning this interval give you? added 105 characters in body Jun 22 answered How much information does learning this interval give you? Jun 20 revised What are some Applications of Hermitian Positive Definite matrices? added 1 character in body Jun 20 revised What are some Applications of Hermitian Positive Definite matrices? edited body Jun 20 revised What are some Applications of Hermitian Positive Definite matrices? added 2 characters in body Jun 20 answered What are some Applications of Hermitian Positive Definite matrices? Jun 17 accepted What property of a matrix causes $\|e^{tA}\|_2$ to oscillate as $t\rightarrow\infty$? Jun 16 comment Solving a matrix equation using numerical optimization You can without loss of generality assume that $A$ is symmetric. if $A$ is not positive semi-definite then the function is not bounded below and so the minimum is $-\infty$. Jun 14 comment Density function of a transformation $P(Y < a) = P(X^3 < a ) = P(X < \sqrt[3]{a})$