29 - Image

Image

Let $V,W$ be vector spaces
Let $T:V\to W$ be linear

$$\mathrm{Im}T:=\{T(v)\mid v\in V\}$$

In other words, $\ker T$ contains vectors that are sent to $0_W$ by the map $T$

Rank

Let $V,W$ be vector spaces with $V$ finite-dimensional
Let $T:V\to W$ be linear

$$\mathrm{rank}(T):=\dim (\mathrm{Im}T)$$

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