Operator norm

In mathematics, the operator norm measures the "size" of certain linear operators by assigning each a real number called its operator norm. Formally, it is a norm defined on the space of bounded linear operators between two given normed vector spaces. Informally, the operator norm ${\displaystyle \|T\|}$ of a linear map ${\displaystyle T:X\to Y}$ is the maximum factor by which it "lengthens" vectors.