Matrix multiplication as composition | Essence of linear algebra, chapter 4
Multiplying two matrices represents applying one transformation after another. Many facts about matrix multiplication become much clearer once you digest this ...
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It is my experience that proofs involving matrices can be shortened by 50% if one throws matrices out. -- Emil Artin Hey everyone! Where we last left off, I showed what linear transformations look like and how to represent them using matrices. This is worth a quick recap, because it's just really important. But of course, if this feels like more than just a recap, go back and watch the full video. Technically speaking, linear transformations are functions, with vectors as inputs and vectors as outputs. But I showed last time how we can think about them visually as smooshing around space in such a way the gridlines stay parallel and evenly spaced, and so that the origin remains fixed. The key take-away was that a linear transformation is completely determined, by where it takes the...
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It is my experience that proofs involving matrices can be shortened by 50% if one throws matrices out. -- Emil Artin Hey everyone! Where we last left off, I showed what linear transformations look like and how to represent them using matrices. This is worth a quick recap, because it's just really important. But of course, if this feels like more than just a recap, go back and watch the full video. Technically speaking, linear transformations are functions, with vectors as inputs and vectors as outputs. But I showed last time how we can think about them visually as smooshing around space in such a way the gridlines stay parallel and evenly spaced, and so that the origin remains fixed. The key take-away was that a linear transformation is completely determined, by where it takes the...
