The Matrix Transpose: Visual Intuition
Let's look at what the transpose of a matrix means intuitively. We'll understand how the transpose of a matrix is needed for trying to find pairs of vectors that have the same dot product before and after some linear transformation. We'll also use the Singular Value Decomposition to get a better geometric intuition for how these transformations appear geometrically. #matrix #linearalgebra #transpose #svd
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Great use of manim with very clear explanations. Might be better if one could add how Singular Value Decomposition is applied on certain subject.
7.1I think it was a nicely presented video. For me, the novelty was a little lacking, which is of course a challenge when taking on such a well-known topic. I guess it's missing some deeper connection to make it interesting to people who have already studied linear algebra. In the version of this video ideal for me, there would explicit discussion of adjoints and the fundamental theorem of linear algebra (relating ranges of matrices and kernels of their transposes). However, I would guess that your version is more appealing.
6.4Well done. Definitely in the spirit of 3Blue1Brown and not just in his use of Manim. This would be very nice to show my Linear Algebra students at the end of the course when we study orthogonal and symmetric matrices.
7.7This was a great and clear video. I really enjoyed watching it. The geometric representations after the mathematical derivation were really helpful for fully understanding the concepts. I think this is a great video. I recommend using some images or text at moments like the end of the 'Orthogonal Matrices' chapter or at the beginning of the 'What if A is not Invertible' section because it can be confusing to see a black screen (I had to check if my screen was off or something). Again, congratulations and thanks for such a good video. I hope you continue making this kind of content.
9Very nicely animated and explained
7.6