Category:Linear Isomorphisms
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This category contains results about Linear Isomorphisms.
Definitions specific to this category can be found in Definitions/Linear Isomorphisms.
Let $\GF \in \set {\R, \C}$.
Let $X$ and $Y$ be normed vector spaces over $\GF$.
Let $T : X \to Y$ be a bijective bounded linear transformation.
We say that $T$ is a linear isomorphism if and only if it is invertible as a bounded linear transformation.
That is, a bijective linear transformation is a linear isomorphism if and only if it is bounded with bounded inverse.
If there exists a linear isomorphism $T : X \to Y$, we say that $X$ and $Y$ are (linearly) isomorphic.
Pages in category "Linear Isomorphisms"
This category contains only the following page.