Let A be a square matrix of size n whose entries are real or complex numbers. Suppose that the diagonal entires of A are much larger than the size of the other entires in the same row, in the sense that, for each row i, n 2||ai||||aj|| = ||ai1|| + ··· + ||ari|| + ··· . j=1 Prove that A is invertible. + ||ain||.

Let A be a square matrix of size n whose entries are real or complex numbers. Suppose that the diagonal entires of A are much larger than the size of the other entires in the same row, in the sense that, for each row i, n 2||ai||||aj|| = ||ai1|| + ··· + ||ari|| + ··· . j=1 Prove that A is invertible. + ||ain||.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.6: Matrices

Problem 25E: Let A and B be square matrices of order n over Prove or disprove that the product AB is a diagonal...

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