Jordan normal form
Canonical matrix representation
Jordan normal form is a way of representing a square matrix that reveals its fundamental structure.
Any matrix over the complex numbers can be transformed into block-diagonal form, where each block (a Jordan block) has a single eigenvalue on the diagonal and ones on the superdiagonal.
The form is unique up to reordering of blocks, making it canonical for classifying matrices by their algebraic properties.
It generalizes diagonalization to matrices that cannot be fully diagonalized.
- eigenvalueScalar satisfying determinant equation
- eigenvectorDirection preserved under transformation
- matrixOrdered numerical arrangement
- canonicalAccepted as standard
- diagonalSlanting line or path
block · invariant · subspace · linear algebra · transformation · basis · similarity · decomposition · chain · rank · defect · triangular · spectral · reduction · kernel
- linear algebramatrix, linear equation, vectors, linear function, matrices
- Normal FormsDNF
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