Matrix Spaces, Rank 1 matrices, and Small World Graphs
In this lecture on matrix spaces, rank 1 matrices, and small world graphs, the concept of vector spaces is extended to include matrices and differential equations. The rank of matrices, particularly rank 1 matrices, is discussed in detail, and it is shown that every rank 1 matrix can be written as a row times a column. The lecture also explores examples of subspaces, their dimensions, and bases, including those of symmetric and upper triangular matrices. Finally, the idea that rank 1 matrices are the building blocks for all matrices is introduced.
Matrix Spaces, Rank 1 matrices, and Small World Graphs -- Lecture 11. Some more discussion of matrices, bases, dimensions, and vector spaces. Rank of matrices (and rank 1 matrices) are also discussed.
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.
More info at: http://ocw.mit.edu/terms
- What are matrix spaces?
- What is a rank 1 matrix?
- What is the solution space?
- What is a small world graph with nodes and edges?
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Staff Review
This lesson explains very much more the topics from lecture 10. Much is clarified in this lesson, and topics such as dimenion, rank, basis, and vector (or matrix) spaces are discussed in depth. Small world graphs with nodes and edges are also introduced.
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