The determinant | Essence of linear algebra, chapter 5
The determinant of a linear transformation measures how much areas/volumes change during the transformation. Full series: http://3b1b.co/eola Future series ...
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Hello, hello again. So, moving forward I will be assuming you have a visual understanding of linear transformations and how they're represented with matrices the way I have been talking about in the last few videos. If you think about a couple of these linear transformations you might notice how some of them seem to stretch space out while others squish it on in. One thing that turns out to be pretty useful to understanding one of these transformations is to measure exactly how much it stretches or squishes things. More specifically to measure the factor by which the given region increases or decreases. For example look at the matrix with the columns 3, 0 and 0, 2 It scales i-hat by a factor of 3 and scales j-hat by a factor of 2 Now, if we focus our attention on the one by one s...
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Hello, hello again. So, moving forward I will be assuming you have a visual understanding of linear transformations and how they're represented with matrices the way I have been talking about in the last few videos. If you think about a couple of these linear transformations you might notice how some of them seem to stretch space out while others squish it on in. One thing that turns out to be pretty useful to understanding one of these transformations is to measure exactly how much it stretches or squishes things. More specifically to measure the factor by which the given region increases or decreases. For example look at the matrix with the columns 3, 0 and 0, 2 It scales i-hat by a factor of 3 and scales j-hat by a factor of 2 Now, if we focus our attention on the one by one s...
