Definition:Linear Transformation of Finite Index

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Let $U, V$ be vector spaces over a field $K$.

Let $T: U \to V$ be a linear transformation.

$T$ is said to have finite index if and only if:

$\paren 1$ $\map \ker T$ is finite-dimensional
$\paren 2$ the quotient space $V / \Img T$ is finite-dimensional


$\map \ker T$ denotes the kernel of $T$
$\Img T$ denotes the image of $T$

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