Show that the condition number of an invertible matrix must be at least 1. What matrices have
condition number equal to 1.
If someone could help me with this and give an explanation that would be very helpful. I do not know where to start
[Math] Prove condition number of a invertible matrix is atleast one
linear algebra
Best Answer
Hint: note that $\|AB\| \leq \|A\|\cdot \|B\|$ (that is, $\|\cdot\|$ is "sub-multiplicative").
So, $\|A\|\cdot \|A^{-1}\| \geq \cdots ?$