Abstract
In the previous section, we utilized the orthogonal direct-sum decomposi- tions
and
where\( V_1 = Sp(A),W_1 = {V_1}^ \bot,W_2 = Ker(A),\)and\( V_2 = {W_2}^{\bot,}\)to define the Moore-Penrose inverseA- of the n by m matrix A in \( y = Ax \) a linear transformation from \( E^m \,\) to \( E^n\, \) Let \( A \prime \) be a matrix that represents a linear transformation \( x = A \prime y \) from \( E^n \) to \( E^m \).Then the following theorem holds.
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© 2011 Springer Science+Business Media, LLC
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Yanai, H., Takeuchi, K., Takane, Y. (2011). Singular Value Decomposition (SVD). In: Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition. Statistics for Social and Behavioral Sciences. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9887-3_5
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DOI: https://doi.org/10.1007/978-1-4419-9887-3_5
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