A linear transformation is determined by how it acts on a basis

Let $T:V\to W$ be a linear transformation, and $\{v_i\}_{i\in I}$ be a basis for $V$, and let $\{w_i\}_{i\in V}$ be any vectors in $W$. Then there's an unique linear transformation $T$ such that $Tv_1=w_1$ for all $i$.

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Related

A linear transformation is determined by how it acts on a basis

Let $T:V\to W$ be a linear transformation, and $\{v_i\}_{i\in I}$ be a basis for $V$, and let $\{w_i\}_{i\in V}$ be any vectors in $W$. Then there's an unique linear transformation $T$ such that $Tv_1=w_1$ for all $i$.

Concepts

Coming soon

Hypothesis

Coming soon

Results

Coming soon

Proof

Coming soon

Related