## Elements of the theory of generalized inverses for matrices |

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### Contents

SYSTEMS OF EQUATIONS AND THE MOOREPENROSE | 9 |

MORE ON MOOREPENROSE INVERSES 2 9 | 29 |

DRAZIN INVERSES | 57 |

Copyright | |

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Ak-l Ak-l AX)H basis of N(A Bw)d column vector Compute conditions AXA conjugate transpose consistent system construct a matrix corresponding to eigenvalue CS(A defining equations denote design of experiments eigenvectors equations Ax equations in 2.2 Example 5.l exists full column rank full rank factorization full row rank G3W G3W Given Hermitian holds I-AA+)b implies inverses of matrices Kronecker product least squares solution left inverse Lemma l0 minimal norm solution monograph Moore-Penrose inverse Moreover nonsingular nonsingular matrix normal matrix null matrix Observe obtained by permuting orthogonal orthonormal basis particular solution permutation matrices permuting rows plane positive integer Proof Prove rank C,B real number right inverse scalar solution of Ax square matrix system of equations tableau Theorem 9 tions transportation problem unique matrix unique solution upper trapezoidal W-weighted Drazin inverse written XA)H