Calculate the inverse of a matrix

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amine&& 2016-9-14

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https://ww2.mathworks.cn/matlabcentral/answers/303062-calculate-the-inverse-of-a-matrix

编辑： Valentin Marinov 2021-1-23

采纳的回答： John D'Errico

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Hello, i want to calculate the reverse of this matrix :

  -1     0     0
-1     1     0     0
   0     1    -1
   0    -1     1

but I get the following result :

   Inf   Inf   Inf   Inf
   Inf   Inf   Inf   Inf
   Inf   Inf   Inf   Inf
   Inf   Inf   Inf   Inf

what are your suggestion? Thanks.

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Brendan Hamm 2016-9-14

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This is a singular matrix, as can be seen by the linear dependence of columns:

X(:,1) == -X(:,2)

and

X(:,3) == -X(:,4)

amine&& 2016-9-14

Thanks Brendan. Yes i understand you're is a singular matrix, therefore its inverse can not calculate but we can calculate a pseudo-inverse.

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John D'Errico 2016-9-14

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This is a singular matrix. No matter how badly you want to do so, you cannot invert a singular matrix. Not possible. Never will be. The laws of mathematics are simple in this respect. The inverse does not exist. You cannot form what does not exist.

At best, you can use pinv, to compute a pseudo-inverse. It is NOT an inverse. It does not have the properties of an inverse.

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amine&& 2021-1-22

@Valentin Marinov thanks for the joke. Can you give the definition of the Moore–Penrose inverse.

Valentin Marinov 2021-1-23

编辑：Valentin Marinov 2021-1-23

Sure. Here's a video that explains it good enough: https://www.youtube.com/watch?v=5bxsxM2UTb4. The example is at 3:30. I'm no pro so don't think I know how to use this in real life, but the guy explains the idea pretty good and tells the matlab funtions, you can use to simulate the actions he explains. Hope it helps you out.

EDIT: just saw the post is from 2016, so I assume you don't need that anymore, but I'll leave it just in case.

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