The set of self adjoint operators admits a partial order, in which $A \ge B$ if $A − B \ge 0$. If A is Hermitian and ⟨ $Ax, x⟩ \ge 0$ for every x, then A is called 'nonnegative', written $A \ge 0$ if equality holds only when x = $\theta$, then A is called 'positive'. Look at the section which says "An element A of B( H) is called 'self-adjoint' or 'Hermitian' if A* = A. What is the reasoning for this? Are there any other examples like this? The same thing applies for the sample standard deviation $s$ and the sample variance $s^2$. The population variance is simply noted as $\sigma^2$. However, no symbol was chosen for the variance. The population standard deviation is noted as $\sigma$. The mean of the squares of the deviations from the arithmetic mean of the distribution is called the variance.
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