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From Wikipedia, a Jordan canonical form can be written in terms of its Jordan blocks as :

$$J=J_{a_1}(\lambda_1)\oplus J_{a_2}(\lambda_2)\oplus\cdots\oplus J_{a_n}(\lambda_n), $$

I was wondering what matrix operation $\oplus$ is? Thanks!

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up vote 2 down vote accepted

It's the direct sum of matrices: "Direct Sum of Matrices" at Wikipedia.

To better understand this, you should read about direct sums of vector spaces: "Direct Sum of Modules: Construction for Vector Spaces and Abelian Groups" at Wikipedia.

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Just a remark: sometimes the same notation is used for Kronecker's sum of two matrices. – Artem Nov 26 '12 at 3:37

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