In a textbook, I came across matrix norms induced from vector norms, and it says:
$$ ||A x|| \le ||A||\cdot||x|| $$ $A \in \mathbb{R}^{NxN},\ x \in \mathbb{R}^N$.
May I please ask for a gentle proof on why is this the case?
2026-03-27 00:05:56.1774569956
Why is the norm of a matrix-vector product less than or equal to the product of the matrix and vector norms?
62 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in MATRICES
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