In this linear algebra lesson, the focus is on transposes, permutations, and the introduction to vector spaces. The concept of permutation matrices is explored and how they are used to solve systems of equations. The idea of transposes, and symmetric matrices is introduced, along with their properties. The lesson concludes with the definition of a vector space and examples of vector spaces such as R2.
Transposes, Permutations, Spaces R^n -- Lecture 5. Some more work with transposes and permutation matrices. Also, an introduction into vector spaces.
Gilbert Strang, 18.06 Linear Algebra, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 16, 2008). License: Creative Commons BY-NC-SA.
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Questions answered by this video:
What is a transpose of a matrix?
What is a permutation matrix?
What is a vector space?
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Another good video of undergraduate linear algebra. Watch this video for more help and information after lecture 4.