Multiplication is defined in a way that is not commutative by default, where multiplying a dictionary with a scalar results in each value of the dictionary being multiplied by the scalar
This phrase is confusing: it says that multiplication is not commutative by default (what does "default" mean here?) and then it talks about multiplying dictionaries by scalars as if to illustrate the non-commutativity.
To understand what this means, you need to actually look into the paper and find what is commutative and what is non-commutative.
A reasonable rewrite would be: "Multiplication by scalars is in general non-commutative. (full stop, it's going to be a different topic now!) Multiplying a dictionary with a scalar results in ..."
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Multiplication is defined in a way that is not commutative by default, where multiplying a dictionary with a scalar results in each value of the dictionary being multiplied by the scalar
This phrase is confusing: it says that multiplication is not commutative by default (what does "default" mean here?) and then it talks about multiplying dictionaries by scalars as if to illustrate the non-commutativity.
To understand what this means, you need to actually look into the paper and find what is commutative and what is non-commutative.
A reasonable rewrite would be: "Multiplication by scalars is in general non-commutative. (full stop, it's going to be a different topic now!) Multiplying a dictionary with a scalar results in ..."