2010-2 Nonsingular matrix

Let A=(aij) be an n×n matrix of complex numbers such that \(\displaystyle\sum_{j=1}^n |a_{ij}|<1\) for each i. Prove that I-A is nonsingular.

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2 thoughts on “2010-2 Nonsingular matrix

  1. Passing by

    교수님! \sum_{i =1}^{n}{ | a_{ij} | } < 1 for each j 이거나, \sum_{j = 1}^{n}{|a_{ij|} < 1 for each j 가 맞지 않을까 하고 생각합니다.

    즐거운 설 명절 보내십시오!

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