So , this is the exercise:
Let $f$ be a linear transformation and injective in $\mathbb {R^n}\rightarrow\mathbb{R^m}$. For abuse , let's denote by $\|.\|$ the norm in both sides.Show that exists a constant $c>0$ such that: $\|f(x)\|\geq c\|x\| \forall x \in \mathbb{R^n}$
Someone explainded to me how to do this one, but honestly I didn't understand a thing...If anyone can help me how to get starded , Much appreciated!