" Let $V$ and $W$ be vector spaces over a field $F$, and let $T_V:V\rightarrow V$ and $T_W:W\rightarrow W$ be linear transformations. We define the product transformation $T_V\times T_W:V\times W\rightarrow V\times W$ by $(T_V\times T_W)(v,w)=(T_V(v),T_W(w))$ for
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