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mcyoung.xyz | ||
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hadrienj.github.io
In this post, we will see special kinds of matrix and vectors the diagonal and symmetric matrices, the unit vector and the concept of orthogonality. |
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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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www.jeremykun.com
The singular value decomposition (SVD) of a matrix is a fundamental tool in computer science, data analysis, and statistics. It's used for all kinds of applications from regression to prediction, to finding approximate solutions to optimization problems. In this series of two posts we'll motivate, define, compute, and use the singular value decomposition to analyze some data. (Jump to the second post) I want to spend the first post entirely on motivation and background. |
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www.johnmyleswhite.com
Lately, I've been running a series of fMRI experiments on visual perception. In the interests of understanding the underlying properties of the images I'm using as stimuli, I've been trying to learn more about the matrix transformations commonly used for image compression and image manipulation. Thankfully, R provides simple-to-use implementations for all of the matrix operations I wanted to play around with, so it's been quite easy to get started. For the next few posts, I thought that I'd review the st... |
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