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Let V and W be finite dimensional vector spaces over a field F with dimF(V )...

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Basic Math

Let V and W be finite dimensional vector spaces over a field Fwith dimF(V ) = dimF(W ) and let T : V ? W be a linear map. Provethere exists an ordered basis A for V and an ordered basis B for Wsuch that [T ]AB is a diagonal matrix where every entry along thediagonal is either a 0 or a 1.

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