OMG, where was this article when I was first learning about tensor products?

https://www.math3ma.com/blog/the-tensor-product-demystified

In 10 minutes I learned more about tensor products than I did in grad school. In particular, I see more of the connection between the way math uses tensor products and how physicist types think of them, as higher-dimensional matrices.

This kind of thing really riles me up. It's the kind of thing that makes me want to go back to teaching, because it hits the exact personality/psychological trait that makes me like teaching: I learn about some cool math thing and I want to charge into a classroom and say "GUYS! I just figured this out! It's so cool and interesting! OMG tensor products are the best, let me show you why!"

It bothers me that I was taught about tensor products in such a bad way. I want students to get something better than I did.

(OTOH, maybe I'm just not very smart, or was a bad student. That's a real possibility. But how great would it be for even dim bulbs and lazy students to get *something* out of learning about a topic?)

#math #linearalgebra #mtbos #teaching

Just action game problems, and their delicious linear algebra solutions.

#DotProduct4Life #LinearAlgebra #Unity3D #GameDev

coming back around to this topic… the axiomatic #geometry treatment comes a bit later in Casse, with chapter 3, in contrast with Seidenberg, who constructs the axioms in chapter 2. Casse, having begun with an assumed knowledge in #LinearAlgebra , can provide a richer construction of the axioms (IMO), where Seidenberg gives a more verbose explanation. This verbosity feels “lighter” in content, despite (necessarily! they’re axioms!) landing on the same concepts.

Really this might come down to a difference where, 60 years ago, you were expected to discuss the topic. Nowadays I get the impression you’re expected to *compute* the solutions more readily than discuss them.

@alexshendi
Yeah, #AI is #LinearAlgebra and nothing more...

Earlier, during a study break, I was standing here in front of the university, staring at the wall there. Imagined a 2×3 matrix multiplied by a 3×n matrix and wondered why matrix B had to have as many rows as matrix A had columns, and then I kind of saw it on the wall and started doing the multiplication, and then it was all clear to me. Transformation to Sheldon completed.

#math #maths #mathematics #science #studying #linearalgebra

https://xkcd.com/2813/ #xkcd #Mathematics #LinearAlgebra

Also called #physicist's common sense: whenever you encounter a #matrix, always discard non-diagonal terms.

Makes life simpler.
May provide a fairly good estimate of the result.

Hello fedinerds, got any recommendations for someone with dyscalculia (I can do theory and concepts, not numbers without analogies first) for understanding #entropy (and entropy in nature), #linearalgebra, #statistics, or any other topics of note? Any good YouTube lectures, podcasts, reads, etc.?

an the reason why I picked up my iPhone 45 minutes ago 🙄… I wanted to recommend “Applied Optimal Estimation” by the technical staff at The Analytic Sciences Corporation (pictured).

I read through the first two chapters today, which swiftly review #LinearAlgebra and #ProbabilityTheory , then #LinearDynamicSystems , building steadily towards #autocorrelation and #autoregression , finally topping off with two paragraphs of the fast Fourier transform #FFT

If that sounds like it’s a lot for 90 pages— it is! I really enjoy how concise and lucid the writing is. It’s a technical manual for applied scientists in the mid 1970s. It’s meant to be useful, understandable, and point to further studies if desired. In other words, by reading books like this, I try to rehearse the content at the same time I learn how to present technical information in an accessible manner

Question for people who have studied #LinearAlgebra , have you read the following paper from 1996 by Sheldon Axler(if not you probably read his book Linear Algebra Done Right).

https://www.axler.net/DwD.html

\( \textbf{Abstract}\) : This paper shows how linear algebra can be done better without determinants. The standard proof that a square matrix of complex numbers has an eigenvalue uses determinants.

So are you Down with Determinants ?

Just wanted to share a little milestone on my journey. This morning I got the results for the first module in my Pure #Mathematics BSc degree from the #openuniversity. I've been working hard on that for most of the past year and I really proud that I was awarded a distinction grade.

#Mathematics and other technical topics don't come easily to me so I'm very happy with the result. There's a lot of effort / struggle / time spent behind it. Happy to have had some good role models and encouragement along the way. Looking forward to the next two modules which start formally in October! We get to dive into #linearalgebra and #calculus. Exciting! 🤓

I really should get back to learning #linearalgebra

@chrisoffner3d and don't forget #linearalgebra !

Looking over some highlights from my teaching year. This was a great moment! And it became a part of several conversations (and little research projects) afterwards.

"Introduced projection matrices & asked students to find something interesting about the matrix A. One student had a brilliant observation: She noticed you can write A like this, which shows how the projection is the average of the vector and its reflection!" (From Twitter)

#math #MathEd #LinearAlgebra

It's kind of ironic that ChatGPT is so terrible at Linear Algebra 🤖 🧠 💥 #Vectors #ChatGPT #LinearAlgebra #AI #DataScience

My favorite part of Linear Algebra so far is how at the end of every section they say something like "now, this is not an efficient technique for solving the system but..."

#Math #AppliedMath #LinearAlgebra

#Math #Maths #Mathematics #LinearAlgebra

Anybody know of a source for explicit form of a low-rank update to symmetric square root of a matrix? Like Sherman-Morrison-Woodbury but for (A +U C V’)^{1/2}?

#Stats #math #linearAlgebra

#BigData #AI #Mathematics #Statistics #Algorithms #Probability #LinearAlgebra #StatisticalLearning #SupervisedLearning
Je vous partage ce livre très intéressant, en accès libre (en anglais, au format PDF] :
« #DataScience and #MachineLearning — Mathematical and Statistical Methods ».
https://people.smp.uq.edu.au/DirkKroese/DSML/DSML.pdf

Education advice from legendary VC Jim Breyer just now on #cnbc:

"Forget about learning to code. Learn linear algebra." -- Jim Breyer

#linearalgebra #math #machinelearning

References
--------------
[1] "Breyer Capital", https://breyercapital.com/

"But when will I ever use this?"

Finding the crew makeup that satisfies personnel ratios for a given crew size, by solving 3 equations with matrices and row operations.

I never thought I'd be using linear algebra working for a construction company, but the broader your toolset, the more likely you'll have just the right one for any situation. (Also I'm always thrilled to find uses for the cool stuff I spent a lot of time and money learning. More please)

#Mathematics #LinearAlgebra