In Lecture 12, the focus is on real-world applications of linear algebra, specifically on graphs, networks, and incidence matrices. The discussion centers around a small example graph with four nodes and five edges, and how to create the incidence matrix associated with it. The lesson delves into questions about the null space and rank of the matrix, and also explores the fundamental equation of A transpose Y equals zero. Overall, the lesson provides valuable insights into how linear algebra can be applied to real-world problems.
Graphs, Networks, and Incidence Matrices -- Lecture 12. An in-depth discussion of small real-world graphs and their nodes / edges.
Gilbert Strang, 18.06 Linear Algebra, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 22, 2008). License: Creative Commons BY-NC-SA.
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Questions answered by this video:
What is the node of a graph?
What is the edge of a graph?
What is an example of a real-world directed graph?
What is an incidence matrix?
Currently 4.0/5 Stars.
This is a very real-world oriented video with small directed graphs and incidence matrices describing the nodes and edges of these graphs. This video gives meaning and purpose to matrices.