Category:Definitions/Linear Isometries

This category contains definitions related to Linear Isometries.
Related results can be found in Category:Linear Isometries.

Let $\struct {X, \norm \cdot_X}$ and $\struct {Y, \norm \cdot_Y}$ be normed vector spaces.

Let $T : X \to Y$ be a linear transformation.

We say that $T$ is a linear isometry if and only if:

$\norm {T x}_Y = \norm x_X$

for each $x \in X$.