Permutations | Numerical linear algebra

In-place matrix transposition

In-place matrix transposition, also called in-situ matrix transposition, is the problem of transposing an N×M matrix in-place in computer memory, ideally with O(1) (bounded) additional storage, or at most with additional storage much less than NM. Typically, the matrix is assumed to be stored in row-major or column-major order (i.e., contiguous rows or columns, respectively, arranged consecutively). Performing an in-place transpose (in-situ transpose) is most difficult when N ≠ M, i.e. for a non-square (rectangular) matrix, where it involves a complicated permutation of the data elements, with many cycles of length greater than 2. In contrast, for a square matrix (N = M), all of the cycles are of length 1 or 2, and the transpose can be achieved by a simple loop to swap the upper triangle of the matrix with the lower triangle. Further complications arise if one wishes to maximize memory locality in order to improve cache line utilization or to operate out-of-core (where the matrix does not fit into main memory), since transposes inherently involve non-consecutive memory accesses. The problem of non-square in-place transposition has been studied since at least the late 1950s, and several algorithms are known, including several which attempt to optimize locality for cache, out-of-core, or similar memory-related contexts. (Wikipedia).

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Transpose of matrices

In this very easy and short tutorial I explain the concept of the transpose of matrices, where we exchange rows for columns. The matrices have some properties that you should be aware of. These include how to the the transpose of the product of matrices and in the transpose of the invers

From playlist Introducing linear algebra

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What is the transpose of a matrix?

What is the transpose of a matrix? Here it is defined and some simple examples are discussed. Free ebook http://tinyurl.com/EngMathYT

From playlist Intro to Matrices

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Transpose of a Matrix | Don't Memorise

What is the Transpose of a Matrix? ✅To learn more about, Matrices, enroll in our full course now: https://infinitylearn.com/microcourses?utm_source=youtube&utm_medium=Soical&utm_campaign=DM&utm_content=g_Rz94DXvNo&utm_term=%7Bkeyword%7D In this video, we will learn: 0:00 what is transp

From playlist Matrices

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Ex: Find the Transpose of a Matrix

This video explains how to find the transpose of a given matrix.

From playlist Introduction to Matrices and Matrix Operations

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Transpose of a Matrix

This video defines the transpose of a matrix and explains how to transpose a matrix. The properties of transposed matrices are also discussed. Site: mathispower4u.com Blog: mathispower4u.wordpress.com

From playlist Introduction to Matrices and Matrix Operations

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Transpose matrix | Lecture 4 | Matrix Algebra for Engineers

Definition of the transpose. How to take the transpose of the product of two matrices. Join me on Coursera: https://www.coursera.org/learn/matrix-algebra-engineers Lecture notes at http://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf Subscribe to my channel: http://www.yout

From playlist Matrix Algebra for Engineers

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Matrices: Transpose and Symmetric Matrices

This is the third video of a series from the Worldwide Center of Mathematics explaining the basics of matrices. This video deals with matrix transpose and symmetric matrices. For more math videos, visit our channel or go to www.centerofmath.org

From playlist Basics: Matrices

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Linear Algebra 11w: Introduction to the Transpose of a Matrix

https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep

From playlist Part 1 Linear Algebra: An In-Depth Introduction with a Focus on Applications

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Tensor Transposition — Topic 11 of Machine Learning Foundations

In this video from my Machine Learning Foundations series, I introduce the theory of tensor transposition, and we carry out hands-on demos of transposition in NumPy, TensorFlow, and PyTorch. There are eight subjects covered comprehensively in the ML Foundations series and this video is f

From playlist Linear Algebra for Machine Learning

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GPGPU computing, let's go!

Broadcasted live on Twitch -- Watch live at https://www.twitch.tv/simuleios

From playlist research

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Limit Profiles of Reversible Markov Chains - Evita Nestoridi

Probability Seminar Topic: Limit Profiles of Reversible Markov Chains Speaker: Evita Nestoridi Affiliation: Stony Brook University, Princeton University Date: November 11, 2022 It all began with card shuffling. Diaconis and Shahshahani studied the random transpositions shuffle; pick two

From playlist Mathematics

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Differential Forms | The Hodge operator via an inner product.

We describe how to define a more generalized Hodge operator via an inner product of m-forms. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.com/stores/michael-penn-math Personal Website: http://www.michael-penn.net Randolph College

From playlist Differential Forms

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What's a representation? An intro to modern math's magical machinery | #SoME2

This video is an introduction to the representation theory of finite groups. It is pretty dense, but I did my best not to include much heavy mathematics. I'll leave some links below for some more background on several of the topics in the video. None of these are necessary to understand th

From playlist Summer of Math Exposition 2 videos

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Transpose Definition

Definition of the transpose Have you ever wondered where the transpose comes from? In this video, I show that the transpose arises naturally in the setting of dual spaces. This should also illustrate why dual spaces are so important. Enjoy! Transpose Example (Sequel): https://youtu.be/x2

From playlist Dual Spaces

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Darij Grinberg - The one-sided cycle shuffles in the symmetric group algebra

We study a new family of elements in the group ring of a symmetric group – or, equivalently, a class of ways to shuffle a deck of cards. Fix a positive integer n. Consider the symmetric group S_n. For each 1 ≤ ℓ ≤ n, we define an element t_ℓ := cyc_ℓ + cyc{ℓ,ℓ+1} + cyc_{ℓ,ℓ+1,ℓ+2} + · · ·

From playlist Combinatorics and Arithmetic for Physics: Special Days 2022

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Differential Forms | The Minkowski metric and the Hodge operator.

We explore the lifting of the Minkowski inner product to the space of 2 and 3 forms. Then we look at what effect this has on the corresponding Hodge operator. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.com/stores/michael-penn-ma

From playlist Differential Forms

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Linear Algebra - Part 32 - Transposition for Matrices

Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths Or support me via PayPal: https://paypal.me/brightmaths Or via Ko-fi: https://ko-fi.com/thebrightsideofmathematics Or via Patreon: https://www.patreon.com/bsom Or via other methods: https://thebrightsideofmathematics.

From playlist Linear Algebra

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Christian Gaetz: "Antichains and intervals in the weak order"

Asymptotic Algebraic Combinatorics 2020 "Antichains and intervals in the weak order" Christian Gaetz - Massachusetts Institute of Technology Abstract: The weak order is the partial order on the symmetric group S_n (or other Coxeter group) whose cover relations correspond to simple transp

From playlist Asymptotic Algebraic Combinatorics 2020

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