Matrices | Algebraic graph theory

Seidel adjacency matrix

In mathematics, in graph theory, the Seidel adjacency matrix of a simple undirected graph G is a symmetric matrix with a row and column for each vertex, having 0 on the diagonal, −1 for positions whose rows and columns correspond to adjacent vertices, and +1 for positions corresponding to non-adjacent vertices.It is also called the Seidel matrix or—its original name—the (−1,1,0)-adjacency matrix. It can be interpreted as the result of subtracting the adjacency matrix of G from the adjacency matrix of the complement of G. The multiset of eigenvalues of this matrix is called the Seidel spectrum. The Seidel matrix was introduced by J. H. van Lint and in 1966 and extensively exploited by Seidel and coauthors. The Seidel matrix of G is also the adjacency matrix of a signed complete graph KG in which the edges of G are negative and the edges not in G are positive. It is also the adjacency matrix of the two-graph associated with G and KG. The eigenvalue properties of the Seidel matrix are valuable in the study of strongly regular graphs. (Wikipedia).

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Adjugate Matrix

In this video, I define the notion of adjugate matrix and use it to calculate A-1 using determinants. This is again beautiful in theory, but inefficient in examples. Adjugate matrix example: https://youtu.be/OFykHi0idnQ Check out my Determinants Playlist: https://www.youtube.com/playlist

From playlist Determinants

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Graph Representation with an Adjacency Matrix | Graph Theory, Adjaceny Matrices

How do we represent graphs using adjacency matrices? That is the subject of today's graph theory lesson! We will take a graph and use an adjacency matrix to represent it! It is a most soulless, but at times useful, graph representation. An adjacency matrix has a row and a column for each

From playlist Graph Theory

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Section 3b Adjacency Matrix and Incidence Matrix

This video is about Section 3b Adjacency Matrix and Incidence Matrix

From playlist Graph Theory

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Dihedral group example

In this veideo we continue our look in to the dihedral groups, specifically, the dihedral group with six elements. We note that two of the permutation in the group are special in that they commute with all the other elements in the group. In the next video I'll show you that these two el

From playlist Abstract algebra

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The Identity Matrix

This video introduces the identity matrix and illustrates the properties of the identity matrix. http://mathispower4u.yolasite.com/ http://mathispower4u.wordpress.com/

From playlist Introduction to Matrices and Matrix Operations

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Computational Methods for Numerical Relativity, Part 1 Frans Pretorius

Computational Methods for Numerical Relativity, Part 1 Frans Pretorius Princeton University July 16, 2009

From playlist PiTP 2009

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Lecture: Eigen-decompositions and Iterations

We develop a theoretical approach to understanding how eigen-decompositions of matrices can be used in iterative schemes for Ax=b.

From playlist Beginning Scientific Computing

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CMPSC/Math 451. March 20, 2015. Gauss-Seidel, SOR. Wen Shen

Wen Shen, Penn State University Lectures are based on my book: "An Introduction to Numerical Computation", published by World Scientific, 2016. See promo video: https://youtu.be/MgS33HcgA_I

From playlist Numerical Computation spring 2015. Wen Shen. Penn State University.

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CMPSC/Math 451. March 23, 2015. Error analysis of iterative methods. Least squares. Wen Shen

Wen Shen, Penn State University. Lectures are based on my book: "An Introduction to Numerical Computation", published by World Scientific, 2016. See promo video: https://youtu.be/MgS33HcgA_I

From playlist Numerical Computation spring 2015. Wen Shen. Penn State University.

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Graph Representation part 02 - Adjacency Matrix

See complete series on data structures here: http://www.youtube.com/playlist?list=PL2_aWCzGMAwI3W_JlcBbtYTwiQSsOTa6P In this lesson, we have talked about Adjacency Matrix representation of Graph and analyzed its time and space complexity of adjacency matrix representation. Previous Less

From playlist Data structures

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Mod-01 Lec-29 Gauss-Seidel Method

Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in

From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics

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Lec 15 | MIT 18.086 Mathematical Methods for Engineers II

Iterative Methods and Preconditioners View the complete course at: http://ocw.mit.edu/18-086S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 18.086 Mathematical Methods for Engineers II, Spring '06

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Sine of a Matrix

Today, we define the sine of a matrix as well as go through an example.

From playlist Linear Algebra

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ch7 5. Iterative Solvers. Linear Fixed Point Iteration for systems. Wen Shen

Wen Shen, Penn State University. Lectures are based on my book: "An Introduction to Numerical Computation", published by World Scientific, 2016. See promo video: https://youtu.be/MgS33HcgA_I

From playlist CMPSC/MATH 451 Videos. Wen Shen, Penn State University

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matrix choose a matrix

matrix choose a matrix. Calculating the number of matrix combinations of a matrix, using techniques from linear algebra like diagonalization, eigenvalues, eigenvectors. Special appearance by simultaneous diagonalizability and commuting matrices. In the end, I mention the general case using

From playlist Eigenvalues

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Martin Gander: On the invention of iterative methods for linear systems

HYBRID EVENT Recorded during the meeting "1Numerical Methods and Scientific Computing" the November 9, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on

From playlist Numerical Analysis and Scientific Computing

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Lec 16 | MIT 18.086 Mathematical Methods for Engineers II

General Methods for Sparse Systems View the complete course at: http://ocw.mit.edu/18-086S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 18.086 Mathematical Methods for Engineers II, Spring '06

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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

Related pages

Graph theory | Multiset | Adjacency matrix | Graph (discrete mathematics) | Mathematics | Two-graph | Strongly regular graph | Complement graph | Signed graph | Symmetric matrix