In this linear algebra lesson, the concept of the four fundamental subspaces is introduced. These subspaces include the column space, null space, row space, and left null space of a matrix. The dimension of each subspace is discussed, with the column space and row space having the same dimension and the null space and left null space having dimensions determined by the number of free variables. A basis for each subspace is also given, with the column space having a basis of pivot columns and the null space having a basis of special solutions.
The Four Fundamental Subspaces -- Lecture 10. Learn what the four fundamental subspaces are.
Gilbert Strang, 18.06 Linear Algebra, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 19, 2008). License: Creative Commons BY-NC-SA.
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