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In vector spaces we define two operations, addition and scalar multiplication. Scalar multiplication is distributive over addition. This can define the order of operations in the vector space? I mean when we have an expression to calculate, we know that we firstly calculate multiplications and after that addition because of this fact? Or is it also a convention? Generally multiplication precedes addition and this also applies to expressions inside parentheses? (we also define that parentheses are calculated before anything else?)

Thanks

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# Vector Space operations

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