#linearalgebra — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #linearalgebra, aggregated by home.social.
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Alright, future engineers!
The **Dot Product** takes two vectors and returns a scalar. It tells you how much they align!
Ex: For `v=[v1,v2]` & `w=[w1,w2]`, `v.w = v1w1 + v2w2`.
Pro-Tip: If `v.w = 0`, the vectors are orthogonal (perpendicular)!
#LinearAlgebra #Vectors #STEM #StudyNotes -
Alright, future engineers!
The **Determinant** of a square matrix is a scalar value that tells you if the matrix is invertible.
Ex: For `[[a,b],[c,d]]`, `det = ad - bc`.
Pro-Tip: If `det = 0`, the matrix is singular (no inverse), meaning `Ax=b` has no unique solution! -
Alright, future engineers!
**Condition Number:** Measures how sensitive a system's solution is to small changes in input data. Ex: High # for Ax=b means small 'b' error can cause large 'x' error. Pro-Tip: A high # means your problem is ill-conditioned—solutions might be unreliable!
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Notes from the 2025 BLIS retreat.
https://www.cs.utexas.edu/~flame/BLISRetreat2025/Talks.html
#blis #hpc #supercomputing #appliedmath #linearalgebra #math #statistics
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💊IronPill 2💊
In the second of our series of short videos ("ironPills") showcasing ironArray's work, we see how Blosc2 can be used to power heavy-duty linear algebra (100GB!) workflows
⚡1.5-2x faster than PyTorch + h5py!
🧱 automated chunking optimised for your machine's cache hierarchy
🐍 simple one-line syntax 𝚋𝚕𝚘𝚜𝚌𝟸.𝚖𝚊𝚝𝚖𝚞𝚕(𝙰, 𝙱, 𝚞𝚛𝚕𝚙𝚊𝚝𝚑='𝚘𝚞𝚝.𝚋𝟸𝚗𝚍')See blog here: https://ironarray.io/blog/la-blosc
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An Illustrated Introduction to Linear Algebra
https://www.ducktyped.org/p/an-illustrated-introduction-to-linear
#HackerNews #An #Illustrated #Introduction #to #Linear #Algebra #linearalgebra #illustration #math #education #learning
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📢🚨Blosc2 3.9.1 Released! 🚨 📢
With this release we further extend array API standard (https://data-apis.org/array-api/latest/index.html) compliance, adding around 70 new functions, methods and attributes 🔝🔝🔝 .
This includes:
• Memory-optimised linear algebra routines: tensordot can be up to 12x 𝐅𝐀𝐒𝐓𝐄𝐑 than NumPy for large arrays 🧱!
• Optimised numerical computation routines ⏩ : functions like hypot are 10x 𝐅𝐀𝐒𝐓𝐄𝐑⚡than NumPy!See here for benchmarks: https://ironarray.io/blog/array-api
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`His initial intended uses were for linguistic analysis and other mathematical subjects like card shuffling, but both Markov chains and matrices rapidly found use in other fields.`
https://en.wikipedia.org/wiki/Stochastic_matrix#History
#AndreyMarkov #Markov #MarkovChain #MarkovModel #statistics #stochastic #stochasticProcess #randomWalk #statisticalPhysics #physics #inference #distribution #equilibrium #transitionRate #transitionMatrix #MarkovMatrix #stochasticMatrix #linearAlgebra #differentialEquation #equation
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#AcademicJob | #PhDStudentship
@ Queen Mary University of London
Understanding Learning Dynamics of Neural Audio Models Using Linear Algebra.
Research focuses on Music Source Separation, Low Rank matrices, and Mechanistic Interpretability in Digital Audio.
https://www.c4dm.eecs.qmul.ac.uk/news/2024-11-12.PhD-call-2025/
Deadline: 29/01/2025
#MusicScience #ComputationalMusicProcessing #ComputationalMusicology #neuralnetworks #MusicTech #DigitalAudio #LinearAlgebra
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Data returned by an observation typically is represented as a vector in machine learning.
A neural network can be seen as a large collection of linear models. We may represent the inputs and outputs of each layer as vectors, matrices, and tensors (which are like higher dimensional matrices).
#algebra #linearAlgebra #vectors #matrices #determinants #singularity #ML #DataScience #math #maths #mathematics #mathStodon #ML #data #dataDon #dataScience #machineLearning #DeepLearning #neuralNetworks
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Evaluating the operator norms of matrices
New blog post on Freedom Math DanceLet E and F be normed vector spaces, over the real or complex numbers, and let u :E→F be a linear map. The continuity of uu is proved to be equivalent to the existence of a real number cc such that ∥u(x)∥≤c∥x∥ for every x∈E, and the least such real number is called the operator norm of uu; we denote it by ∥u∥. It defines a norm on the linear space L(E;F) of continuous linear maps from E to F and as such is quite important. When E=F, it is also related to the spectrum of uu and is implicitly at the heart of criteria for the Gershgorin criterion for localization of eigenvalues.
However, even in the simplest cases of matrices, its explicit computation is not trivial at all, and as we'll see even less trivial than what is told in algebra classes, as I learned by browsing Wikipedia when I wanted to prepare a class on the topic.
Follow the link to read… →
https://freedommathdance.blogspot.com/2024/04/evaluating-operator-norms-of-matrices.html -
Evaluating the operator norms of matrices
New blog post on Freedom Math DanceLet E and F be normed vector spaces, over the real or complex numbers, and let u :E→F be a linear map. The continuity of uu is proved to be equivalent to the existence of a real number cc such that ∥u(x)∥≤c∥x∥ for every x∈E, and the least such real number is called the operator norm of uu; we denote it by ∥u∥. It defines a norm on the linear space L(E;F) of continuous linear maps from E to F and as such is quite important. When E=F, it is also related to the spectrum of uu and is implicitly at the heart of criteria for the Gershgorin criterion for localization of eigenvalues.
However, even in the simplest cases of matrices, its explicit computation is not trivial at all, and as we'll see even less trivial than what is told in algebra classes, as I learned by browsing Wikipedia when I wanted to prepare a class on the topic.
Follow the link to read… →
https://freedommathdance.blogspot.com/2024/04/evaluating-operator-norms-of-matrices.html -
Evaluating the operator norms of matrices
New blog post on Freedom Math DanceLet E and F be normed vector spaces, over the real or complex numbers, and let u :E→F be a linear map. The continuity of uu is proved to be equivalent to the existence of a real number cc such that ∥u(x)∥≤c∥x∥ for every x∈E, and the least such real number is called the operator norm of uu; we denote it by ∥u∥. It defines a norm on the linear space L(E;F) of continuous linear maps from E to F and as such is quite important. When E=F, it is also related to the spectrum of uu and is implicitly at the heart of criteria for the Gershgorin criterion for localization of eigenvalues.
However, even in the simplest cases of matrices, its explicit computation is not trivial at all, and as we'll see even less trivial than what is told in algebra classes, as I learned by browsing Wikipedia when I wanted to prepare a class on the topic.
Follow the link to read… →
https://freedommathdance.blogspot.com/2024/04/evaluating-operator-norms-of-matrices.html -
Evaluating the operator norms of matrices
New blog post on Freedom Math DanceLet E and F be normed vector spaces, over the real or complex numbers, and let u :E→F be a linear map. The continuity of uu is proved to be equivalent to the existence of a real number cc such that ∥u(x)∥≤c∥x∥ for every x∈E, and the least such real number is called the operator norm of uu; we denote it by ∥u∥. It defines a norm on the linear space L(E;F) of continuous linear maps from E to F and as such is quite important. When E=F, it is also related to the spectrum of uu and is implicitly at the heart of criteria for the Gershgorin criterion for localization of eigenvalues.
However, even in the simplest cases of matrices, its explicit computation is not trivial at all, and as we'll see even less trivial than what is told in algebra classes, as I learned by browsing Wikipedia when I wanted to prepare a class on the topic.
Follow the link to read… →
https://freedommathdance.blogspot.com/2024/04/evaluating-operator-norms-of-matrices.html -
Evaluating the operator norms of matrices
New blog post on Freedom Math DanceLet E and F be normed vector spaces, over the real or complex numbers, and let u :E→F be a linear map. The continuity of uu is proved to be equivalent to the existence of a real number cc such that ∥u(x)∥≤c∥x∥ for every x∈E, and the least such real number is called the operator norm of uu; we denote it by ∥u∥. It defines a norm on the linear space L(E;F) of continuous linear maps from E to F and as such is quite important. When E=F, it is also related to the spectrum of uu and is implicitly at the heart of criteria for the Gershgorin criterion for localization of eigenvalues.
However, even in the simplest cases of matrices, its explicit computation is not trivial at all, and as we'll see even less trivial than what is told in algebra classes, as I learned by browsing Wikipedia when I wanted to prepare a class on the topic.
Follow the link to read… →
https://freedommathdance.blogspot.com/2024/04/evaluating-operator-norms-of-matrices.html -
It’s been a week so a #reintroduction now with more #hashtags
I am naura. Been here a week and looks like i am here to stay. born and grew up in #SoCal. I am in the #SFbayarea right now. I am in my 40s and a stay at home mom.
Some hobbies i’ve had are processing wool using the #spinningwheel, #knitting, #crocheting, #crossstitching, #drawing, #cooking -
My only consistent fandom has been #StarTrek. My favorite is #StarTrekVOY and i am a die hard JC shipper. Right now i need #warehouse13 to be rebooted!!!!!
I also love #math specifically #linearAlgebra and #differentialEquations visually.
I guess that’s it for now :)
#LateDignosedADHD. #MajorDepressiveDisorder
#Medicated
#endthestigma -
youtube.com/@xenaproject
for #mathematics #mathsbasics#mathematicallogic #sets #logic #topology #numbertheory #linearalgebra
#probability #measuretheory
#functionalanalysis -
👋 Ma(th)stodon friends! #Introduction
I’m an #AppliedMathematician doing #consulting, #research, and writing on two forthcoming books.
Research interests: #MathematicalDataScience, #TensorDecompositions, #NumericalOptimization, #LinearAlgebra, #NetworkScience, #RandomizedAlgorithms, #MachineLearning, #HPC, …
Champion for #diverity, #equity, and #inclusion (#dei) in the mathematical sciences and #STEM at large.
Other Interests: #AIFailures #LaTeX #TikZ #PGFPlots #Yoga & (literary) #SciFi
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Did not expect to find these kinds of books at an anime convention 🤔 I’m impressed! 🤩
#datascience #dataanalytics #linearalgebra #regressionanalysis #cryptography #databases
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Third Time’s a Charm for This Basketball-Catching Robot - We all know that version one of a project is usually a stinker, at least in retrospect. Sure, it g... - https://hackaday.com/2020/09/09/third-times-a-charm-for-this-basketball-catching-robot/ #linearalgebra #kinecthacks #basketball #mischacks #backboard #cartesian #tracking #corexy #kinect
