For a matrix $X$, a generalized inverse of $X$ is any matrix $Y$ such that $XYX = X$. We use $X^{-}$ to indicate a generalized inverse of $X$. Suppose $X$ is a matrix. $X^{\prime}$ denotes the transpose of $X$. Then clearly $X^{\prime}X$ is symmetric and has a generalized inverse that is symmetr...

So, $$1,1,2,3,5,8,13,21...$$ Any connection to primes?...it appears not. However, in between the Fibonacci numbers are how much primes? Let's see: 1 and 1 ZERO 1 and 2 NADA 2 and 3 ZILCH 3 and 5 ZIP 5 and 8 1 8 and 13 1 13 and 21 2 21 and 34 3 34 and 55 5 55 and 89 8 89 and 144 13 Hu...

We want to show that $\sup(A)+\sup(B)$ is the least upper bound of the set $A + B$. First, we need to show that $\sup(A) + \sup(B)$ is an upper bound for the set $A + B$. Indeed, if $z\in A + B$, then there exists $a\in A$ and $b\in B$ such that $z = a + b$. But by definition of $\sup(A)$ and $\s...