Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, sets, lists, vectors, matrices and tensors. Maxima yields high precision numerical results by using exact fractions, arbitrary-precision integers and variable-precision fl
講義のオフィス・アワーの余談
Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares
Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares Stephen Boyd and Lieven Vandenberghe Cambridge University Press This book is used as the textbook for our own courses ENGR108 (Stanford) and EE133A (UCLA), where you will find additional related material. If you find an error not listed in our
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LAPACK is a software package provided by Univ. of Tennessee; Univ. of California, Berkeley; Univ. of Colorado Denver; and NAG Ltd.. LAPACK is written in Fortran 90 and provides routines for solving systems of simultaneous linear equations, least-squares solutions of linear systems of equations, eigenvalue problems, and singular value problems. The associated matrix factorizations (LU, Cholesky, QR
The-Art-of-Linear-Algebra/The-Art-of-Linear-Algebra.pdf at main · kenjihiranabe/The-Art-of-Linear-Algebra
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Instructor: Prof. Gilbert Strang This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other discip...
The BLAS (Basic Linear Algebra Subprograms) are routines that provide standard building blocks for performing basic vector and matrix operations. The Level 1 BLAS perform scalar, vector and vector-vector operations, the Level 2 BLAS perform matrix-vector operations, and the Level 3 BLAS perform matrix-matrix operations. Because the BLAS are efficient, portable, and widely available, they are commo
numerical-linear-algebra/README.md at master · fastai/numerical-linear-algebra
This course is focused on the question: How do we do matrix computations with acceptable speed and acceptable accuracy? This course was taught in the University of San Francisco's Masters of Science in Analytics program, summer 2017 (for graduate students studying to become data scientists). The course is taught in Python with Jupyter Notebooks, using libraries such as Scikit-Learn and Numpy for m
Unexplanations: sql is syntactic sugar for relational algebra
Unexplanations: sql is syntactic sugar for relational algebra This idea is particularly sticky because it was more or less true 50 years ago, and it's a passable mental model to use when learning sql. But it's an inadequate mental model for building new sql frontends, designing new query languages, or writing tools likes ORMs that abstract over sql. Before we get into that, we first have to figure
Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares
Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares Stephen Boyd and Lieven Vandenberghe Cambridge University Press This book is used as the textbook for our own courses ENGR108 (Stanford) and EE133A (UCLA), where you will find additional related material. If you find an error not listed in our
Basic Linear Algebra Subprograms（BLAS）は数値線形代数の基礎的演算に必要な関数を定義するAPIである[3]。ベクトル・行列演算を含む38の関数からなるLevel 1 BLASが1979年に発表されたのち[4]、Level 2 および Level 3 まで拡張された。多数の実装が作成・整備され続けており、この分野におけるデファクトスタンダードとなっている。BLASの基礎演算を利用してLAPACKなどの上位パッケージが構築されており、科学技術計算・高性能計算で多用される。 BLASの関数を多用するソフトウェアにおいてBLAS実装（ライブラリ）の質は速度に直結する。高度な最適化は実装が動くハードウェアに依存するため、多くのハードウェアベンダーが自社デバイスに特化したライブラリを提供している（インテル：Intel oneAPI Math Kernel Libra
Lecture 1: The Geometry of Linear Equations. View the complete course at: http://ocw.mit.edu/18-06S05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Armadillo: C++ library for linear algebra & scientific computing
Armadillo C++ library for linear algebra & scientific computing Armadillo is a high quality linear algebra library (matrix maths) for the C++ language, aiming towards a good balance between speed and ease of use Provides high-level syntax and functionality deliberately similar to Matlab Useful for algorithm development directly in C++, or quick conversion of research code into production environme
Automatically Tuned Linear Algebra Software (ATLAS)
The ATLAS (Automatically Tuned Linear Algebra Software) project is an ongoing research effort focusing on applying empirical techniques in order to provide portable performance. At present, it provides C and Fortran77 interfaces to a portably efficient BLAS implementation, as well as a few routines from LAPACK. If you download the software, it is critically important that you check the ATLAS errat
Welcome to GAP - Groups, Algorithms, Programming - a System for Computational Discrete Algebra The current version is GAP 4.12.2 released on 18 December 2022. What is GAP? GAP is a system for computational discrete algebra, with particular emphasis on Computational Group Theory. GAP provides a programming language, a library of thousands of functions implementing algebraic algorithms written in th
What is REDUCE? REDUCE is a portable general-purpose computer algebra system. It is a system for doing scalar, vector and matrix algebra by computer, which also supports arbitrary precision numerical approximation and interfaces to gnuplot to provide graphics. It can be used interactively for simple calculations (as illustrated in the screenshot below) but also provides a full programming language
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This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.
Video Lectures | Linear Algebra | Mathematics | MIT OpenCourseWare
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ViennaCL - Linear Algebra Library using CUDA, OpenCL, and OpenMP
ViennaCL is a free open-source linear algebra library for computations on many-core architectures (GPUs, MIC) and multi-core CPUs. The library is written in C++ and supports CUDA, OpenCL, and OpenMP (including switches at runtime). The highlights of the latest 1.7.x release family are: Fast sparse matrix-matrix multiplications, outperforming CUBLAS and MKL.Fine-grained parallel algebraic multigrid
The algebra (and calculus!) of algebraic data types
The algebra (and calculus!) of algebraic data types Joel Burget Note: This article assumes some introductory Haskell knowledge. Introduction Just as algebra is fundamental to the whole of mathematics, algebraic data types (ADTs) are fundamental to many common functional programming languages. They’re the primitives upon which all of our richer data structures are built, including everything from s
数学が苦手な人は数式を組み立てたり、それを解くのが苦手ではないでしょうか。方程式を作って、それを解くのはパズルみたいなものですが、嫌いな人にとっては数字やXなどを見るだけで嫌気がさすはずです。 そんな方に見て欲しいのがalgebra.jsです。なんとJavaScriptを使って方程式を組み立てたり、それを解いてしまうソフトウェアです。 algebra.jsの使い方 algebra.jsでは若干特別な入力を行います。そしてtoString()メソッドで式が文字列で返ってきます。 式は後から追加していくことも可能です。 そしてsolveForで回答を得られます。 変数が複数あっても余裕です。 2次方程式を解く例です。 答えが複数あるなんて場合にも対応しています。 LaTeX向けにビジュアル化された式を表示できます。 algebra.jsの使い方を覚えればかなり難しい数式でも解くことができるので
The Algebra of Algebraic Data Types, Part I - Chris Taylor
I gave a talk on this subject at London Haskell in November 2012. A video of the talk is on YouTube and slides are on GitHub. In this series of posts I’ll explain why Haskell’s data types are called algebraic - without mentioning category theory or advanced math. The algebra you learned in high school starts with numbers (e.g. 1, 2, 3 …) and operators (e.g. addition and multiplication). The operat
During Jeremy Howard’s excellent deep learning course I realized I was a little rusty on the prerequisites and my fuzziness was impacting my ability to understand concepts like backpropagation. I decided to put together a few wiki pages on these topics to improve my understanding. Here is a very basic intro to some of the more common linear algebra operations used in deep learning. NEW: check out
The algebra (and calculus!) of algebraic data types
The algebra (and calculus!) of algebraic data types Joel Burget Note: This article assumes some introductory Haskell knowledge. Introduction Just as algebra is fundamental to the whole of mathematics, algebraic data types (ADTs) are fundamental to many common functional programming languages. They’re the primitives upon which all of our richer data structures are built, including everything from s
AGCA - Algebraic Geometry and Commutative Algebra Module - SymPy 1.12.1 documentation
AGCA - Algebraic Geometry and Commutative Algebra Module¶ Introduction¶ Algebraic geometry is a mixture of the ideas of two Mediterranean cultures. It is the superposition of the Arab science of the lightening calculation of the solutions of equations over the Greek art of position and shape. This tapestry was originally woven on European soil and is still being refined under the influence of inte
GitHub - fastai/numerical-linear-algebra: Free online textbook of Jupyter notebooks for fast.ai Computational Linear Algebra course
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Despite two linear algebra classes, my knowledge consisted of “Matrices, determinants, eigen something something”. Why? Well, let’s try this course format: Name the course Linear Algebra but focus on things called matrices and vectors Teach concepts like Row/Column order with mnemonics instead of explaining the reasoning Favor abstract examples (2d vectors! 3d vectors!) and avoid real-world topics
algebra.js by nicolewhite
algebra.js Build, display, and solve algebraic equations in JavaScript. View on GitHub Download .min.js Quick Start var expr = new Expression("x"); expr = expr.subtract(3); expr = expr.add("x"); console.log(expr.toString());
In numerical linear algebra we are concerned with solving linear algebra problems accurately and efficiently and understanding the sensitivity of the problems to perturbations. We describe seven sins, whereby accuracy or efficiency is lost or misleading information about sensitivity is obtained. In linear algebra courses we learn that the solution to a linear system of equations in unknowns can be
Applications are open for the ACT Applied Category Theory Research School 2018! And because arithmetic science and geometric science are connected, and support one another, the full knowledge of numbers cannot be presented without encountering some geometry, or without seeing that operating in this way on numbers is close to geometry; the method is full of many proofs and demonstrations that are m
The-Art-of-Linear-Algebra/The-Art-of-Linear-Algebra-j.pdf at main · kenjihiranabe/The-Art-of-Linear-Algebra
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Introduction to Linear Algebra
Please choose one of the following, to be redirected to that book's website Introduction to Linear Algebra, 5th Edition (2016 edition) Introduction to Linear Algebra, 6th Edition (2023 edition) Accessibility
The Magma Computational Algebra system for alg ebra, number theory and geometry.Magma is a large, well-supported software package designed to solve computationally hard problems in algebra, number theory, geometry and combinatorics. It provides a mathematically rigorous environment for computing with algebraic, number-theoretic, combinatoric, and geometric objects. Latest version: V2.14-16 (releas
If $A$ is an $n \times n$ Hermitian matrix with eigenvalues $\lambda_1(A),\dots,\lambda_n(A)$ and $i,j = 1,\dots,n$, then the $j^{\mathrm{th}}$ component $v_{i,j}$ of a unit eigenvector $v_i$ associated to the eigenvalue $\lambda_i(A)$ is related to the eigenvalues $\lambda_1(M_j),\dots,\lambda_{n-1}(M_j)$ of the minor $M_j$ of $A$ formed by removing the $j^{\mathrm{th}}$ row and column by the for
These are lecture notes that are based on the lectures from a class I taught on the topic of Randomized Linear Algebra (RLA) at UC Berkeley during the Fall 2013 semester.
The following tables provide a comparison of computer algebra systems (CAS).[1][2][3] A CAS is a package comprising a set of algorithms for performing symbolic manipulations on algebraic objects, a language to implement them, and an environment in which to use the language.[4][5] A CAS may include a user interface and graphics capability; and to be effective may require a large library of algorith
Algebra on Ruby
Rubyを用いた代数計算 Home - 研究 概要 Rubyで代数計算を行うためのパッケージであり、 具体的には、代数系を実装する基本になるプログラム(ring.rb)と、 いくつかの付加的プログラム(以下付加プログラム)と、 いくつかのサンプルプログラムからなります。 付加プログラムを利用すると、以下の代数系を実装できます。 テンソル代数、多項式環 (付加プログラム不要) ワイル代数 (weylalg.rb) 全行列環のなすリー代数の包絡環 (liegl.rb) E6, E7 型単純リー代数の包絡環 (liee6.rb, liee7.rb) 特徴としては、ほとんど全てのRubyのオブジェクトが代数系の元として 使用できることと、 生成系と交換関係式で代数系を定義できることがあげられます。 比較的簡単な代数しか扱えず、 機能も少なく、因数分解もグレブナ基底も計算できませんが、 付加プログ
Linear Algebra Done Right
Linear Algebra Done Right Sheldon Axler I am happy to announce publication of the fourth edition of Linear Algebra Done Right as an Open Access book. The electronic version of this new fourth edition with a Creative Commons BY-NC license is availble without cost at the link below. PDF file for Linear Algebra Done Right, fourth edition (25 March 2024) The print version of the new fourth edition of
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Maxima, a Computer Algebra System
線形代数というものの見方 / View from Linear Algebra
GitHub - rails/arel: A Relational Algebra
LAPACK — Linear Algebra PACKage
MIT 18.06 Linear Algebra, Spring 2005
BLAS (Basic Linear Algebra Subprograms)
Basic Linear Algebra Subprograms - Wikipedia
YouTube - Lec 1 | MIT 18.06 Linear Algebra, Spring 2005
GAP System for Computational Discrete Algebra
REDUCE Computer Algebra System
Mathway | Algebra Problem Solver
Linear Algebra | Mathematics | MIT OpenCourseWare
algebra.js - JavaScriptで数式を解く！ MOONGIFT
Linear algebra cheat sheet for deep learning
An Intuitive Guide to Linear Algebra – BetterExplained
Seven Sins of Numerical Linear Algebra
Graphical Linear Algebra
Magma Computational Algebra System Home Page
Eigenvectors from eigenvalues: A survey of a basic identity in linear algebra
Lecture Notes on Randomized Linear Algebra
List of computer algebra systems - Wikipedia