We will use matrices to perform three distinct classes of operations.
In fact, these operations are all duals of one another, but experience
suggests that it is best to first understand these operations separately.
We can use a matrix to transform one vector to another:
We can use a matrix to change basis vectors:
And, we can use a matrix to change coordinates:
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Once more, some illustrations may help in understanding these distinctions:
(Click on the images below)
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