Warning: this chapter is not for the faint of heart. Linear transformations are not for the faint of mind. They are for those who dare to venture into the depths of mathematical madness.
In the last chapter, we explored the realm of advanced differential calculus, where the unknown became known. But what happens when we take the unknown and apply a series of transformations to it? Welcome to the world of advanced vector calculus, where the rules are made to be broken, and the transformations are made to be... well, made.
Linear transformations are the bread and butter of vector calculus. They are the tools that allow us to take a vector, any vector, and apply a series of transformations to it. But don't be fooled, my friends, these transformations are not to be taken lightly. They are the key to unlocking the secrets of the unknown, but also the key to unlocking your sanity.
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