In mathematics, a balanced matrix is a 0-1 matrix (a matrix where every entry is either zero or one) that does not contain any square submatrix of odd order having all row sums and all column sums equal to 2. Balanced matrices are studied in linear programming. The importance of balanced matrices comes from the fact that the solution to a linear programming problem is integral if its matrix of coefficients is balanced and its right hand side or its objective vector is an all-one vector. In particular, if one searches for an integral solution to a linear program of this kind, it is not necessary to explicitly solve an integer linear program, but it suffices to find an optimal vertex solution of the linear program itself. As an example, the following matrix is a balanced matrix: (Wikipedia).
What is a matrix? Free ebook http://tinyurl.com/EngMathYT
From playlist Intro to Matrices
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
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
This video defines a diagonal matrix and then explains how to determine the inverse of a diagonal matrix (if possible) and how to raise a diagonal matrix to a power. Site: mathispower4u.com Blog: mathispower4u.wordpress.com
From playlist Introduction to Matrices and Matrix Operations
This video is brought to you by the Quantitative Analysis Institute at Wellesley College. The material is best viewed as part of the online resources that organize the content and include questions for checking understanding: https://www.wellesley.edu/qai/onlineresources
From playlist Tutorials for R Statistical Software
The Diagonalization of Matrices
This video explains the process of diagonalization of a matrix.
From playlist The Diagonalization of Matrices
This video defines elementary matrices and then provides several examples of determining if a given matrix is an elementary matrix. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Augmented Matrices
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
Polynomial Identity Testing via Optimization: algorithms by Rafael Oliveira
Discussion Meeting Workshop on Algebraic Complexity Theory  ORGANIZERS Prahladh Harsha, Ramprasad Saptharishi and Srikanth Srinivasan DATE & TIME 25 March 2019 to 29 March 2019 VENUE Madhava Lecture Hall, ICTS Bangalore Algebraic complexity aims at understanding the computationa
From playlist Workshop on Algebraic Complexity Theory 2019
How to Quickly Create a Matrix in GeoGebra; How to Multiply 2 Matrices
Creating a matrix in GeoGebra is EASY. You need to use the LIST icons { }. In GeoGebra, a matrix is actually a sequence of lists within a single list. This video shows how.
From playlist Algebra 1: Dynamic Interactives!
Non-negatively Weighted #CSPs: An Effective Complexity Dichotomy - Xi Chen
Xi Chen Columbia University March 28, 2011 We prove a complexity dichotomy theorem for all non-negatively weighted counting Constraint Satisfaction Problems (#CSP). This caps a long series of important results on counting problems including unweighted and weighted graph homomorphisms and t
From playlist Mathematics
Lec 13 | MIT 18.085 Computational Science and Engineering I, Fall 2008
Lecture 13: Kirchhoff's Current Law License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 18.085 Computational Science & Engineering I, Fall 2008
Leonardo Ermann - Google matrix analysis of the World Trade Network
https://indico.math.cnrs.fr/event/3475/attachments/2180/2565/Ermann_GomaxSlides.pdf
From playlist Google matrix: fundamentals, applications and beyond
(ML 18.6) Detailed balance (a.k.a. Reversibility)
Definition of detailed balance, and an intuitive way to visualize what it means. Detailed balance implies a stationary distribution. Detailed balance = reversibility. Reversibility for stationary Markov chains.
From playlist Machine Learning
Lec 8 | MIT 18.085 Computational Science and Engineering I, Fall 2008
Lecture 08: Springs and masses; the main framework License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 18.085 Computational Science & Engineering I, Fall 2008
Data-Driven Control: Balanced Proper Orthogonal Decomposition
In this lecture, we introduce the balancing proper orthogonal decomposition (BPOD) to approximate balanced truncation for high-dimensional systems. https://www.eigensteve.com/
From playlist Data-Driven Control with Machine Learning
Lec 3 | MIT 18.085 Computational Science and Engineering I
Network applications: A = incidence matrix A more recent version of this course is available at: http://ocw.mit.edu/18-085f08 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 18.085 Computational Science & Engineering I, Fall 2007
Lec 2 | MIT 18.085 Computational Science and Engineering I
One-dimensional applications: A = difference matrix A more recent version of this course is available at: http://ocw.mit.edu/18-085f08 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 18.085 Computational Science & Engineering I, Fall 2007
Data-Driven Control: Balanced Truncation
In this lecture, we describe the balanced truncation procedure for model reduction, where a handful of the most controllable and observable state directions are kept for the reduced-order model. https://www.eigensteve.com/
From playlist Data-Driven Control with Machine Learning