An MDS matrix (maximum distance separable) is a matrix representing a function with certain diffusion properties that have useful applications in cryptography. Technically, an matrix over a finite field is an MDS matrix if it is the transformation matrix of a linear transformation from to such that no two different -tuples of the form coincide in or more components.Equivalently, the set of all -tuples is an MDS code, i.e., a linear code that reaches the Singleton bound. Let be the matrix obtained by joining the identity matrix to . Then a necessary and sufficient condition for a matrix to be MDS is that every possible submatrix obtained by removing rows from is non-singular. This is also equivalent to the following: all the sub-determinants of the matrix are non-zero. Then a binary matrix (namely over the field with two elements) is never MDS unless it has only one row or only one column with all components . Reed–Solomon codes have the MDS property and are frequently used to obtain the MDS matrices used in cryptographic algorithms. Serge Vaudenay suggested using MDS matrices in cryptographic primitives to produce what he called multipermutations, not-necessarily linear functions with this same property. These functions have what he called perfect diffusion: changing of the inputs changes at least of the outputs. He showed how to exploit imperfect diffusion to cryptanalyze functions that are not multipermutations. MDS matrices are used for diffusion in such block ciphers as AES, SHARK, Square, Twofish, Anubis, KHAZAD, , Hierocrypt, Kalyna and Camellia, and in the stream cipher MUGI and the cryptographic hash function Whirlpool. (Wikipedia).
Linear Algebra for Computer Scientists. 12. Introducing the Matrix
This computer science video is one of a series of lessons about linear algebra for computer scientists. This video introduces the concept of a matrix. A matrix is a rectangular or square, two dimensional array of numbers, symbols, or expressions. A matrix is also classed a second order
From playlist Linear Algebra for Computer Scientists
What is a matrix? Free ebook http://tinyurl.com/EngMathYT
From playlist Intro to Matrices
Understanding Matrices and Matrix Notation
In order to do linear algebra, we will have to know how to use matrices. So what's a matrix? It's just an array of numbers listed in a grid of particular dimensions that can represent the coefficients and constants from a system of linear equations. They're fun, I promise! Let's just start
From playlist Mathematics (All Of It)
2 Construction of a Matrix-YouTube sharing.mov
This video shows you how a matrix is constructed from a set of linear equations. It helps you understand where the various elements in a matrix comes from.
From playlist Linear Algebra
Identity Matrix | Unit Matrix | Don't Memorise
This video explains the concept of an Identity Matrix. Is it also called a Unit 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=iks8wCfPerU&utm_term=%7Bkeyword%
From playlist Matrices
Matrix Addition, Subtraction, and Scalar Multiplication
This video shows how to add, subtract and perform scalar multiplication with matrices. http://mathispower4u.yolasite.com/ http://mathispower4u.wordpress.com/
From playlist Introduction to Matrices and Matrix Operations
We have already looked at the column view of a matrix. In this video lecture I want to expand on this topic to show you that each matrix has a column space. If a matrix is part of a linear system then a linear combination of the columns creates a column space. The vector created by the
From playlist Introducing linear algebra
Definition of a matrix | Lecture 1 | Matrix Algebra for Engineers
What is a matrix? 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/jchasnov?sub_confirmation=1
From playlist Matrix Algebra for Engineers
Lec 10 | MIT 6.451 Principles of Digital Communication II
Reed-Solomon Codes View the complete course: http://ocw.mit.edu/6-451S05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.451 Principles of Digital Communication II
Doing MDS (multi-dimensional scaling) and PCoA (principal coordinate analysis) is pretty easy with the cmdscale() option. However, there are some tricks to it and I show you how to create a distance matrix using a non-standard distance metric. If you want the code that I used in this vide
From playlist Statistics and Machine Learning in R
Multidimensional Scaling - An EXTREMELY POWERFUL algorithm
Entry to #some2 Multidimensional scaling is also similar to PCA and has other names as well. I hope this video informs you of the basics. You can probably analyse a clean dataset using it now if you know some R or Python. Top 1000 Instagram Influencer dataset: https://www.kaggle.com/d
From playlist Summer of Math Exposition 2 videos
08c Machine Learning: Multidimensional Scaling
Lecture on multidimensional scaling for feature projection. Reduce the dimensionality while preserving the dissimilarity between the training samples. Follow along with the demonstration workflow in Python's scikit-learn package: https://github.com/GeostatsGuy/PythonNumericalDemos/blob/ma
From playlist Machine Learning
Bala Krishnamoorthy (10/20/20): Dimension reduction: An overview
Bala Krishnamoorthy (10/20/20): Dimension reduction: An overview Title: Dimension reduction: An overview Abstract: We present a broad overview of various dimension reduction techniques. Referred to also as manifold learning, we review linear dimension reduction techniques, e.g., principa
From playlist Tutorials
Noah Giansiracusa (1/20/21): Looking for geometry in the Supreme Court
Title: Looking for geometry in the Supreme Court Abstract: Empirical legal studies is the corner of political science that uses data to better understand various aspects of the court system. The voting behavior of the 9 judges on the bench of the U.S. Supreme Court has been a topic of s
From playlist AATRN 2021
John Maddocks: "The cgDNA sequence-dependent coarse-grain model of dsDNA: Bridging the scales fr..."
Machine Learning for Physics and the Physics of Learning 2019 Workshop III: Validation and Guarantees in Learning Physical Models: from Patterns to Governing Equations to Laws of Nature "The cgDNA sequence-dependent coarse-grain model of dsDNA: Bridging the scales from Molecular Dynamics
From playlist Machine Learning for Physics and the Physics of Learning 2019
Nexus Trimester - P. Vijay Kumar (Indian Institute of Science, University of Southern California)
On Outer Bounds for the Storage-Repair-Bandwidth Tradeoff of Exact-Repair Regenerating Codes P. Vijay Kumar (Indian Institute of Science, University of Southern California) February 19, 2016 Abstract: It has been known for some that it is not possible to achieve the storage-repair bandwi
From playlist Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme
Seminar on Applied Geometry and Algebra (SIAM SAGA): Camilla Hollanti
Date: Tuesday, December 8 at 11:00am EST (5:00pm CET) Speaker: Camilla Hollanti, Aalto University Title: Coding theoretic framework for private information retrieval Abstract: Private information retrieval (PIR) addresses the question of how to retrieve data items from a database or clo
From playlist Seminar on Applied Geometry and Algebra (SIAM SAGA)
Anders Nikklasson - Quantum-Mechanical Molecular Dynamics for Distributed Computing and AI-hardware
Recorded 27 March 2023. Anders Nikklasson of Los Alamos National Laboratory presents "Quantum-Mechanical Molecular Dynamics for Distributed Computing and AI-hardware" at IPAM's Increasing the Length, Time, and Accuracy of Materials Modeling Using Exascale Computing workshop. Abstract: We p
From playlist 2023 Increasing the Length, Time, and Accuracy of Materials Modeling Using Exascale Computing
Matrix Algebra Basics || Matrix Algebra for Beginners
In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. This course is about basics of matrix algebra. Website: https://geekslesson.com/ 0:00 Introduction 0:19 Vectors and Matrices 3:30 Identities and Transposes 5:59 Add
From playlist Algebra