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This tag is for questions relating to the Jordan normal form, also known as a Jordan canonical form or JCF of a matrix which is a similar block matrix having diagonal blocks when the matrix is diagonalizable and diagonal + nilpotent blocks more generally.

The Jordan normal form of a matrix is a canonical form given by a similarity transformation. The Jordan normal form consists of diagonal blocks corresponding to its generalized eigenvectors, with blocks that are themselves constant diagonal when an eigenvalue has a basis of eigenvectors and otherwise blocks that are constant diagonal + nilpotent. For more information, see this Wikipedia article.