# Idempotent matrices in Julia
**URL:** https://discourse.julialang.org/t/idempotent-matrices-in-julia/82467
**Category:** Teaching & Outreach
**Tags:** tutorials, matrices
**Created:** [June 9, 2022, 1:18am UTC](https://discourse.julialang.org/t/idempotent-matrices-in-julia/82467 "2022-06-09T01:18:17Z")
**Posts on this page:** 8
**Page:** 1
### Author:  [@VinodV](https://discourse.julialang.org/u/VinodV)
#### Post date: [June 9, 2022, 1:18am UTC](https://discourse.julialang.org/t/idempotent-matrices-in-julia/82467/1 "2022-06-09T01:18:17Z")
Hi all,
I have created a small blog post related to Idempotent matrices with Julia.
[Idempotent matrices in Julia](https://pythonjulia.blogspot.com/2022/06/idempotent-matrices-in-julia.html)
Please provide your feedback.
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### Author:  [@mcreel](https://discourse.julialang.org/u/mcreel)
#### Post date: [June 9, 2022, 6:17am UTC](https://discourse.julialang.org/t/idempotent-matrices-in-julia/82467/2 "2022-06-09T06:17:46Z")
You could show that rank(A)=tr(A)=4.
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### Author:  [@jd-foster](https://discourse.julialang.org/u/jd-foster)
#### Post date: [June 9, 2022, 7:06am UTC](https://discourse.julialang.org/t/idempotent-matrices-in-julia/82467/3 "2022-06-09T07:06:07Z")
Here is another direction: What if you wanted to have a rank 3 idempotent matrix? How would you find a vector `v` such that `u'*v = 0` so that we can make a `B` with rank(B) = 3 and `B^100 ≈ B`?
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### Author:  [@skleinbo](https://discourse.julialang.org/u/skleinbo)
#### Post date: [June 9, 2022, 7:17am UTC](https://discourse.julialang.org/t/idempotent-matrices-in-julia/82467/4 "2022-06-09T07:17:06Z")
Very nice. I like your 100 Julia Excercises too!
I feel the sentence
> Idempotent matrices behave like identity matrices when raised to a power n
is a bit misleading. They do only after being applied once.
I think your example demonstrates Julia’s natural math syntax nicely and if that’s all you want, then I say well done.
If you want to go a step further and showcase what Julia can do, you could define a `IdempotentMatrix<:AbstractMatrix` type and specialize all kinds of linear algebra on it. Most importantly of course matrix powers, but also eigenvalues, trace, determinant…
I admit that I’ve thought about this for approximately five minutes, so maybe there is good reason not to 😃
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### Author:  [@VinodV](https://discourse.julialang.org/u/VinodV)
#### Post date: [June 9, 2022, 2:39pm UTC](https://discourse.julialang.org/t/idempotent-matrices-in-julia/82467/5 "2022-06-09T14:39:57Z")
> [@skleinbo](#):
>
> Idempotent matrices behave like identity matrices when raised to a power n
What would be a correct sentence which will clearly show the behaviour of idempotent matrices when raised to a power?
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### Author:  [@jacobusmmsmit](https://discourse.julialang.org/u/jacobusmmsmit)
#### Post date: [June 9, 2022, 2:47pm UTC](https://discourse.julialang.org/t/idempotent-matrices-in-julia/82467/6 "2022-06-09T14:47:13Z")
I think `P^2 = P` explains it tbh.
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### Author:  [@skleinbo](https://discourse.julialang.org/u/skleinbo)
#### Post date: [June 9, 2022, 3:32pm UTC](https://discourse.julialang.org/t/idempotent-matrices-in-julia/82467/7 "2022-06-09T15:32:25Z")
I’m with @jacobusmmsmit in this. The definition is perfectly understandable. IMHO the sentence could be left out entirely.
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### Author:  [@VinodV](https://discourse.julialang.org/u/VinodV)
#### Post date: [June 17, 2022, 4:06pm UTC](https://discourse.julialang.org/t/idempotent-matrices-in-julia/82467/8 "2022-06-17T16:06:31Z")
Cross posted to [Idempotent matrices in Julia - Julia Community 🟣](https://forem.julialang.org/vinodv/idempotent-matrices-in-julia-470o)