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Vinod V
Vinod V

Posted on • Updated on • Originally published at pythonjulia.blogspot.com

Idempotent matrices in Julia

Let AA be a square matrix of order nn . Then AA is called an idempotent matrix if AA=AAA = A .

If a matrix AA is idempotent, it follows that An=A,nNA^n = A, \forall n \in \mathbb{N} . All Idempotent matrices except identity matrices are singular matrices.

One way to make idempotent matrices is A=IuuTA = I - u u^T , where uu is a vector satisfying uTu=1u^T u = 1 . In this case AA is symmetric too.

#Idempotent matrices in Julia
using LinearAlgebra
u = rand(5)
u = u/norm(u) #Force u^T * u = 1
A = I - u*u'
isapprox(A^100,A) # true
isequal(A,A') # true (test for symmetricity)
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Cross posted to https://pythonjulia.blogspot.com/2022/03/100-julia-exercises-with-solutions.html

Discussion (3)

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Logan Kilpatrick

Hey! This is cool to see, it would be nice to also add some context for folks about why you would need this, etc etc. You can also set the canonical URL if you edit this post to point to the original blog post above.

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Vinod V Author

You can also set the canonical URL if you edit this post to point to the original blog post above.
How to do it.

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Logan Kilpatrick

I went ahead and fixed it for you, but next to the publish button there's a blue circle-ish thing, that's where you can set the canonical URL.