MathB.in
New
Demo
Tutorial
About
($\implies$) Suppose $A$ is invertible, then $S\subset \Bbb R^n$ $$S=\{h\in\mathbb R^n: \lVert h\rVert=1\}$$ $T:S\to \mathbb R$ $$T(h)=\lVert Ah\rVert>0\quad\forall h\in S.$$ $T(h)\neq 0$ for all $h\in S$. $T(h)$ attains a positive minimum $c$. $$T(h)\geq c\forall h\in S$$ For all $0\neq u\in\mathbb R^n$, there is $h=u/\lVert u\rVert$ such that $$\lVert Au\rVert=\lVert u\rVert \lVert Ah\rVert\geq c\lVert u\rVert$$
ERROR: JavaScript must be enabled to render input!
Sun, 11 Apr 2021 03:45 GMT