Frequently Asked Questions
What is the Moore-Penrose pseudoinverse?
The unique generalization of the matrix inverse that exists for any matrix, square or not. It gives the least-squares solution to Ax = b: x equals A pseudoinverse times b.
When is it equal to the regular inverse?
When A is square and invertible. For a square non-invertible matrix or a rectangular matrix, the pseudoinverse is well-defined but the regular inverse is not.
Why use it in linear regression?
Solving the normal equations beta equals A transpose A inverse times A transpose y is exactly multiplying y by the pseudoinverse of A. It gives the ordinary least squares solution.
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