How to Read a Matrix Expression
Often we desire to apply sequences of operations to vectors.
For instance, we might want to translate a point to the origin,
rotate it about some vector, and then translate it back.
In order to specify and interpret such sequences,
you should become proficient at reading matrix expressions.
The expression
can be read in one of two ways depending
on the associativity of the multiplication.
Associating the left part of the expression
is interpreted as changing the basis while keeping the coordinates fixed
Associating the right part of the expression
is interpreted as changing coordinates while keeping the basis fixed
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