Exercise 5.1.12. Prove that, for every projection matrix P that the projection onto the column space of a matrix A, the matrix I– P is also a projection matrix and it represents the projection onto Left-null(A) = Col(A)-. represents -

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter5: Orthogonality
Section5.4: Orthogonal Diagonalization Of Symmetric Matrices
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Exercise 5.1.12. Prove that, for every projection matrix P that represents
the projection onto the column space of a matrix A, the matrix I – P is
also a projection matrix and it represents the projection onto Left-null(A) =
Col(A)+.
Transcribed Image Text:Exercise 5.1.12. Prove that, for every projection matrix P that represents the projection onto the column space of a matrix A, the matrix I – P is also a projection matrix and it represents the projection onto Left-null(A) = Col(A)+.
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