Boolean algebra | Algebraic logic

Canonical normal form

In Boolean algebra, any Boolean function can be expressed in the canonical disjunctive normal form (CDNF) or minterm canonical form and its dual canonical conjunctive normal form (CCNF) or maxterm canonical form. Other canonical forms include the complete sum of prime implicants or Blake canonical form (and its dual), and the algebraic normal form (also called Zhegalkin or Reed–Muller). Minterms are called products because they are the logical AND of a set of variables, and maxterms are called sums because they are the logical OR of a set of variables. These concepts are dual because of their complementary-symmetry relationship as expressed by De Morgan's laws. Two dual canonical forms of any Boolean function are a "sum of minterms" and a "product of maxterms." The term "Sum of Products" (SoP or SOP) is widely used for the canonical form that is a disjunction (OR) of minterms. Its De Morgan dual is a "Product of Sums" (PoS or POS) for the canonical form that is a conjunction (AND) of maxterms. These forms can be useful for the simplification of these functions, which is of great importance in the optimization of Boolean formulas in general and digital circuits in particular. (Wikipedia).

Video thumbnail

Example of Rational Canonical Form 2: Several Blocks

Matrix Theory: Let A be a 12x12 real matrix with characteristic polynomial (x^2+1)^6, minimal polynomial (x^2 + 1)^3, and dim(Null(A^2 + I)) = 6. Find all possible rational canonical forms for A.

From playlist Matrix Theory

Video thumbnail

Example of Rational Canonical Form 3

Matrix Theory: We note two formulations of Rational Canonical Form. A recipe is given for combining and decomposing companion matrices using cyclic vectors.

From playlist Matrix Theory

Video thumbnail

Example of Rational Canonical Form 1: Single Block

Matrix Theory: Let A be the real matrix [0 -1 1 0 \ 1 0 0 1 \ 0 0 0 -1 \ 0 0 1 0]. Find a matrix P that puts A into rational canonical form over the real numbers. We compare RCF with Jordan canonical form and review companion matrices. (Minor corrections added.)

From playlist Matrix Theory

Video thumbnail

F[x]-Module Derivation of Rational and Jordan Canonical Forms

Similar matrices isomorphism proof: https://youtu.be/-ligAAxFM8Y Every module is a direct sum of cyclic modules: https://youtu.be/gWIRI43h0ic Intro to F[x]-modules: https://youtu.be/H44q_Urmts0 The rational canonical form and Jordan normal form of a matrix are very important tools in li

From playlist Ring & Module Theory

Video thumbnail

The Normal Distribution (1 of 3: Introductory definition)

More resources available at www.misterwootube.com

From playlist The Normal Distribution

Video thumbnail

Unicode Normalization for NLP in Python

ℕ𝕠-π• π•Ÿπ•– π•šπ•Ÿ π•₯π•™π•–π•šπ•£ π•£π•šπ•˜π•™π•₯ π•žπ•šπ•Ÿπ•• 𝕨𝕠𝕦𝕝𝕕 𝕖𝕧𝕖𝕣 𝕦𝕀𝕖 π•₯𝕙𝕖𝕀𝕖 π•’π•Ÿπ•Ÿπ• π•ͺπ•šπ•Ÿπ•˜ π•—π• π•Ÿπ•₯ π•§π•’π•£π•šπ•’π•Ÿπ•₯𝕀. 𝕋𝕙𝕖 𝕨𝕠𝕣𝕀π•₯ π•₯π•™π•šπ•Ÿπ•˜, π•šπ•€ π•šπ•— π•ͺ𝕠𝕦 𝕕𝕠 π•’π•Ÿπ•ͺ π•—π• π•£π•ž 𝕠𝕗 ℕ𝕃ℙ π•’π•Ÿπ•• π•ͺ𝕠𝕦 𝕙𝕒𝕧𝕖 𝕔𝕙𝕒𝕣𝕒𝕔π•₯𝕖𝕣𝕀 π•π•šπ•œπ•– π•₯π•™π•šπ•€ π•šπ•Ÿ π•ͺ𝕠𝕦𝕣 π•šπ•Ÿπ•‘π•¦π•₯, π•ͺ𝕠𝕦𝕣 π•₯𝕖𝕩π•₯ π•“π•–π•”π• π•žπ•–π•€ π•”π• π•žπ•‘π•π•–π•₯𝕖𝕝π•ͺ π•¦π•Ÿπ•£π•–π•’π••π•’π•“π•π•–. We also find that text like this is incredibly commonβ€Š-β€Šparticularly on social me

From playlist Recommended

Video thumbnail

Alexander Soibelman - Quantizations of Complex Lagrangian Fibrations, Normal Forms, and Spectra

Under certain conditions, it is possible to compute the spectrum of a polynomial differential operator via its Birkhoff normal form. In this talk, I will explain a geometric approach for obtaining the Birkhoff normal form of a quantized Hamiltonian using the variation of Hodge structure fo

From playlist Workshop on Quantum Geometry

Video thumbnail

R. Berman - Canonical metrics, random point processes and tropicalization

In this talk I will present a survey of the connections between canonical metrics and random point processes on a complex algebraic variety X. When the variety X has positive Kodaira dimension, this leads to a probabilistic construction of the canonical metric on X introduced by Tsuji and

From playlist Complex analytic and differential geometry - a conference in honor of Jean-Pierre Demailly - 6-9 juin 2017

Video thumbnail

Carolina Araujo: - Fano Foliations 1 -Definition, examples and first properties

CIRM VIRTUAL EVENT Recorded during the research school "Geometry and Dynamics of Foliations " the May 11, 2020 by the Centre International de Rencontres MathΓ©matiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on C

From playlist Virtual Conference

Video thumbnail

Weil-Petersson currents by Georg Schumacher

DISCUSSION MEETING ANALYTIC AND ALGEBRAIC GEOMETRY DATE:19 March 2018 to 24 March 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore. Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions be

From playlist Analytic and Algebraic Geometry-2018

Video thumbnail

Introduction to the Principal Unit Normal Vector

Introduction to the Principal Unit Normal Vector

From playlist Calculus 3

Video thumbnail

J. V. Pereira - Algebraic leaves of codimension one foliations (Part 2)

This mini-course will review old and new results about algebraic leaves of codimension one foliations on projective manifolds. I will discuss some of the following topics: Darboux's Theorem and generalizations; compact leaves; holonomy of an algebraic leaf; and effective algebraic integrat

From playlist Ecole d'Γ©tΓ© 2019 - Foliations and algebraic geometry

Video thumbnail

Tests, Games, and Martin-Lof's Meaning Explanations for Intuitionistic Type Theory - Peter Dybjer

Peter Dybjer November 30, 2012 For more videos, visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Overview of Jordan Canonical Form

Matrix Theory: We give an overview of the construction of Jordan canonical form for an nxn matrix A. The main step is the choice of basis that yields JCF. An example is given with two distinct eigenvalues.

From playlist Matrix Theory

Related pages

Disjunctive normal form | Conjunctive normal form | Algebraic normal form | Product term | De Morgan's laws | Canonical form | Logical disjunction | Boolean function | Logical conjunction | Truth table | Blake canonical form | List of Boolean algebra topics | Karnaugh map