Prove that for any matrix A ∈ Mm×n(F), (R(LA∗))⊥= N(LA).
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.6: Matrices
Problem 21E: Suppose that A is an invertible matrix over and O is a zero matrix. Prove that if AX=O, then X=O.
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Prove that for any matrix A ∈ Mm×n(F), (R(LA∗))⊥= N(LA).
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