The Four Fundamental Subspaces and Least Squares
Description
The four subspaces are the column spaces and the nullspaces of A and A^T: two perpendicular subspaces in *m-*dimensional space and two more in n-dimensional space. A is invertible when m = n and both nullspaces contain only the zero vector.
When A is NOT invertible, we look for the vector x in the row space that makes || Ax - b || AS SMALL AS POSSIBLE in the column space.
This video finds that winning vector! Instead of x = A^-1 b (that inverse doesn’t exist) we introduce the “pseudoinverse” of A.
Slides Used in this Video: The Four Fundamental Subspaces and Least Squares (PDF)
Instructor: Gilbert Strang
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2020
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