- #1

isa_vita

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How to prove the following equation:

(I+A)^-1=I+A/2 ?

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- Thread starter isa_vita
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- #1

isa_vita

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How to prove the following equation:

(I+A)^-1=I+A/2 ?

- #2

HallsofIvy

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(I+ A)(I+ A/2)= I+ A+ A/2+ A^2/2= I+ A+ A/2+ A/2= I+ 2A, not I.

If you mean (I+ A)/2,

(I+ A)(I+ A)/2= (I+ A+ A+ A^2)/2= (I+ 3A)/2.

I thought perhaps you had left out a "-" but that doesn't see to work either so I have no idea what you are trying to prove.

- #3

isa_vita

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You have understood correctly.

As I tried to solve the problem I came to the same answer.

Perhaps there is a technical error, but I'm not sure.

Thanks for answer.

- #4

oli4

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you equation does have a solution: A=0 works, but you would say 'solve' instead of 'prove', so maybe you didn't word it correctly (but it sounds fishy, this would be a weird exercise anyway), so, anyway, do you have the full text of the exercise ?

Cheers...

- #5

isa_vita

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I know for a zero solution, but it isn't the task. I think it is right HallsofIvy. It is a technical error.

Thanks for a help. Cheers...

- #6

HallsofIvy

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- #7

chiro

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- #8

HallsofIvy

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That's exactly what

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