Sparse matrices | Permutations | Matrices
In mathematics, particularly in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column and 0s elsewhere. Each such matrix, say P, represents a permutation of m elements and, when used to multiply another matrix, say A, results in permuting the rows (when pre-multiplying, to form PA) or columns (when post-multiplying, to form AP) of the matrix A. (Wikipedia).
Permutation matrices | Lecture 9 | Matrix Algebra for Engineers
What is a permutation matrix? Define 2x2 and 3x3 permutation 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.youtube.com/user/jch
From playlist Matrix Algebra for Engineers
Permutation Groups and Symmetric Groups | Abstract Algebra
We introduce permutation groups and symmetric groups. We cover some permutation notation, composition of permutations, composition of functions in general, and prove that the permutations of a set make a group (with certain details omitted). #abstractalgebra #grouptheory We will see the
From playlist Abstract Algebra
301.5C Definition and "Stack Notation" for Permutations
What are permutations? They're *bijective functions* from a finite set to itself. They form a group under function composition, and we use "stack notation" to denote them in this video.
From playlist Modern Algebra - Chapter 16 (permutations)
From playlist Sample Midterm
This project was created with Explain Everything™ Interactive Whiteboard for iPad.
From playlist Modern Algebra - Chapter 16 (permutations)
Stanley-Wilf limits are typically exponential - Jacob Fox
Jacob Fox Massachusetts Institute of Technology October 7, 2013 For a permutation p, let Sn(p) be the number of permutations on n letters avoiding p. Stanley and Wilf conjectured that, for each permutation p, Sn(p)1/n tends to a finite limit L(p). Marcus and Tardos proved the Stanley-Wilf
From playlist Mathematics
Learning from ranks, learning to rank - Jean-Philippe Vert, Google Brain
Permutations and sorting operators are ubiquitous in data science, e.g., when one wants to analyze or predict preferences. As discrete combinatorial objects, permutations do not lend themselves easily to differential calculus, which underpins much of modern machine learning. In this talk I
From playlist Statistics and computation
What is a Tensor? Lesson 25: Review of Determinants
What is a Tensor? Lesson 25: Review of Determinants This lesson is purely a review of a mathematical topic that we will need for our upcoming work regarding exterior product spaces and the exterior algebra. If you are solid on determinants then you can skip this lesson
From playlist What is a Tensor?
Learning from permutations. - Vert - Workshop 3 - CEB T1 2019
Jean-Philippe Vert (Mines ParisTech, Google) / 05.04.2019 Learning from permutations. Changes in image quality or illumination may affect the pixel intensities, without affecting the relative intensities, i.e., the ranking of pixels in an image by decreasing intensity. In order to learn
From playlist 2019 - T1 - The Mathematics of Imaging
Topics in Combinatorics lecture 7.4 --- The Marcus-Tardos theorem
We say that a permutation pi of {1,2,...,k} is contained in a permutation sigma of {1,2,...,n} if we can find k elements of {1,2,...,n} that are reordered by sigma in the way that pi reorders {1,2,...,k}. For instance, the permutation 2413 (meaning that 1 goes to 2, 2 goes to 4, 3 goes to
From playlist Topics in Combinatorics (Cambridge Part III course)
Abstract Algebra: (Linear Algebra Required) The symmetric group S_n is realized as a matrix group using permutation matrices. That is, S_n is shown to the isomorphic to a subgroup of O(n), the group of nxn real orthogonal matrices. Applying Cayley's Theorem, we show that every finite gr
From playlist Abstract Algebra
36 entangled officers of Euler: A quantum solution to a classically... by Arul Lakshminarayan
Colloquium: 36 entangled officers of Euler: A quantum solution to a classically impossible problem Speaker: Arul Lakshminarayan (IIT Madras, Chennai) Date: Mon, 06 June 2022, 15:30 to 17:00 Venue: Online and Madhava Lecture Hall Abstract The 36 officers problem of Euler is a well-known i
From playlist ICTS Colloquia
Levi-Civita and Kronecker: A Remarkable Relationship | Deep Dive Maths
There is a remarkable relationship between the product of two Levi-Civita symbols and the determinant of a matrix with the Kronecker delta as elements. After defining the Levi-Civita symbol and the Kronecker delta, I show how to derive this relationship using permutation matrices and the
From playlist Deep Dive Maths
AMMI Course "Geometric Deep Learning" - Lecture 5 (Graphs & Sets I) - Petar Veličković
Video recording of the course "Geometric Deep Learning" taught in the African Master in Machine Intelligence in July-August 2021 by Michael Bronstein (Imperial College/Twitter), Joan Bruna (NYU), Taco Cohen (Qualcomm), and Petar Veličković (DeepMind) Lecture 5: Learning on sets • Permutat
From playlist AMMI Geometric Deep Learning Course - First Edition (2021)