In mathematics, a Boolean matrix is a matrix with entries from a Boolean algebra. When the two-element Boolean algebra is used, the Boolean matrix is called a logical matrix. (In some contexts, particularly computer science, the term "Boolean matrix" implies this restriction.) Let U be a non-trivial Boolean algebra (i.e. with at least two elements). Intersection, union, complementation, and containment of elements is expressed in U. Let V be the collection of n × n matrices that have entries taken from U. Complementation of such a matrix is obtained by complementing each element. The intersection or union of two such matrices is obtained by applying the operation to entries of each pair of elements to obtain the corresponding matrix intersection or union. A matrix is contained in another if each entry of the first is contained in the corresponding entry of the second. The product of two Boolean matrices is expressed as follows: According to one author, "Matrices over an arbitrary Boolean algebra β satisfy most of the properties over β0 = {0, 1}. The reason is that any Boolean algebra is a sub-Boolean algebra of for some set S, and we have an isomorphism from n × n matrices over " (Wikipedia).
From playlist Week 1 2015 Shorts
Boolean Algebra: Sample Problems
In this video, I work through some sample problems relating to Boolean algebra. Specific, I work through examples of translating equivalences from logical or set notation to Boolean notation, and also a derivation using Boolean equivalences.
From playlist Discrete Mathematics
Declare and instantiate a boolean array. Access and modify the array by indices. Print an array using a for-loop.
From playlist Java Programming
Using Boolean in Python (Python Tutorial #11)
Using Boolean in Python - let's go! This entire series in a playlist: https://goo.gl/eVauVX Also, keep in touch on Facebook: https://www.facebook.com/entercsdojo And Twitter: https://twitter.com/ykdojo
From playlist Python Tutorials for Absolute Beginners by CS Dojo
What is a matrix? Free ebook http://tinyurl.com/EngMathYT
From playlist Intro to Matrices
Boolean Algebra 2 – Simplifying Complex Expressions
This video follows on from the one about the laws of Boolean algebra. It explains some useful interpretations of the laws of Boolean algebra, in particular, variations of the annulment and distributive laws. It goes on to demonstrate how Boolean algebra can be applied to simplify comple
From playlist Boolean Algebra
Analysis of Boolean Functions on Association Schemes - Yuval Filmus
Yuval Filmus Member, School of Mathematics September 23, 2014 More videos on http://video.ias.edu
From playlist Mathematics
Boolean Algebra 1 – The Laws of Boolean Algebra
This computer science video is about the laws of Boolean algebra. It briefly considers why these laws are needed, that is to simplify complex Boolean expressions, and then demonstrates how the laws can be derived by examining simple logic circuits and their truth tables. It also shows ho
From playlist Boolean Algebra
Live CEOing Ep 74: Quantum Computing in Wolfram Language
Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Quantum Computing in the Wolfram Language.
From playlist Behind the Scenes in Real-Life Software Design
The Monomial Structure of Boolean Functions - Shachar Lovett
Workshop on Additive Combinatorics and Algebraic Connections Topic: The Monomial Structure of Boolean Functions Speaker: Shachar Lovett Affiliation: University of California, San Diego Date: October 25, 2022 Let f:0,1n to 0,1 be a boolean function. It can be uniquely represented as a mu
From playlist Mathematics
Monotone Arithmetic Circuit Lower Bounds Via Communication Complexity - Arkadev Chattopadhyay
Computer Science/Discrete Mathematics Seminar I Topic: Monotone Arithmetic Circuit Lower Bounds Via Communication Complexity Speaker: Arkadev Chattopadhyay Affiliation: Tata Institute of Fundamental Research Date: February 15, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
A polynomial lower bound for monotonicity testing...- Rocco Servedio
Rocco Servedio Columbia University March 31, 2014 We prove a Ω̃ (n1/5)Ω~(n1/5) lower bound on the query complexity of any non-adaptive two-sided error algorithm for testing whether an unknown n-variable Boolean function is monotone versus constant-far from monotone. This gives an exponenti
From playlist Mathematics
Wolfram Physics Project: Exploring Quantum Computing Tuesday, May 18, 2021
This is a Wolfram Physics Project working session exploring quantum computing in the Wolfram Model. Begins at 6:50 Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the announcemen
From playlist Wolfram Physics Project Livestream Archive
Discrete Math - 9.3.1 Matrix Representations of Relations and Properties
How to represent a relation using a matrix and easy tips for determining if the relation is reflexive, irreflexive, symmetric, antisymetric, asymmetric and transitive. Matrix operations are also reviewed (meet, join and Boolean product). Textbook: Rosen, Discrete Mathematics and Its Appl
From playlist Discrete Math I (Entire Course)
Camille Male - Distributional symmetry of random matrices...
Camille Male - Distributional symmetry of random matrices and the non commutative notions of independence
From playlist Spectral properties of large random objects - Summer school 2017
Introduction to Query-to-Communication Lifting - Mika Goos
Computer Science/Discrete Mathematics Seminar II Topic: Introduction to Query-to-Communication Lifting Speaker: Mika Goos Affiliation: Member, School of Mathematics Date: November 20, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
Strong refutation of semi-random Boolean CSPs - Venkatesan Guruswami
Computer Science/Discrete Mathematics Seminar I Topic: Strong refutation of semi-random Boolean CSPs Speaker: Venkatesan Guruswami Affiliation: Carnegie Mellon University Date: March 08, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
How do we add matrices. A matrix is an abstract object that exists in its own right, and in this sense, it is similar to a natural number, or a complex number, or even a polynomial. Each element in a matrix has an address by way of the row in which it is and the column in which it is. Y
From playlist Introducing linear algebra
Nexus Trimester - Paul Beame (University of Washington) - 1
Branching Programs 1/3 Paul Beame (University of Washington) February 26,2016 Abstract: Branching programs are clean and simple non-uniform models of computation that capture both time and space simultaneously. We present the best methods known for obtaining lower bounds on the size of (l
From playlist Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme