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susam.net | ||
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thatsmaths.com
The numbers are usually studied in layers of increasing subtlety and intricacy. We start with the natural, or counting, numbers $latex {\mathbb{N} = \{ 1, 2, 3, \dots \}}&fg=000000$. Then come the whole numbers or integers, $latex {\mathbb{Z} = \{ \dots, -2, -1, 0, 1, 2, \dots \}}&fg=000000$. All the ratios of these (avoiding division... |
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mcyoung.xyz
[AI summary] This text provides an in-depth explanation of linear algebra concepts, including vector spaces, linear transformations, matrix multiplication, and field extensions. It emphasizes the importance of understanding these concepts through the lens of linear maps and their composition, which naturally leads to the matrix multiplication formula. The text also touches on the distinction between vector spaces and abelian groups, and discusses the concept of field extensions, such as [R:Q] and [C:R]. The author mentions their art blog and acknowledges their own drawing of the content. |
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lisyarus.github.io
[AI summary] The post explores the uniqueness of inverses in mathematical structures, starting with basic number systems and progressing to more complex non-commutative and infinite-dimensional algebras. It explains that while inverses are unique in commutative settings like numbers, they can be non-unique or have directional differences (left/right inverses) in non-commutative contexts. The post highlights that in finite-dimensional algebras, the existence of a left or right inverse implies the existence of the other, ensuring uniqueness, but this doesn't hold in infinite-dimensional cases, where multiple inverses can exist. |
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blog.otoro.net
[AI summary] This article describes a project that combines genetic algorithms, NEAT (NeuroEvolution of Augmenting Topologies), and backpropagation to evolve neural networks for classification tasks. The key components include: 1) Using NEAT to evolve neural networks with various activation functions, 2) Applying backpropagation to optimize the weights of these networks, and 3) Visualizing the results of the evolved networks on different datasets (e.g., XOR, two circles, spiral). The project also includes a web-based demo where users can interact with the system, adjust parameters, and observe the evolution process. The author explores how the genetic algorithm can discover useful features (like squaring inputs) without human intervention, and discusses the ... |
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