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Let () (that is, a n × n complex matrix) and () be the change of basis matrix to the Jordan normal form of A; that is, A = C −1 JC.Now let f (z) be a holomorphic function on an open set such that ; that is, the spectrum of the matrix is contained inside the domain of holomorphy of f.
In linear algebra, a Jordan normal form, also known as a Jordan canonical form, [1] [2] is an upper triangular matrix of a particular form called a Jordan matrix representing a linear operator on a finite-dimensional vector space with respect to some basis.
The Jordan normal form and the Jordan–Chevalley decomposition. Applicable to: square matrix A; Comment: the Jordan normal form generalizes the eigendecomposition to cases where there are repeated eigenvalues and cannot be diagonalized, the Jordan–Chevalley decomposition does this without choosing a basis.
Indeed, it suffices to check this for the decomposition of the Jordan matrix = +. This is a technical argument, but does not require any tricks beyond the Chinese remainder theorem . Proof (Jordan-Chevalley decomposition from Jordan normal form)
3.1.1 Pauli–Jordan function. ... where I 4 is the unit matrix in four dimensions, ... (Has useful appendices of Feynman diagram rules, including propagators, in the ...
A variant of Gaussian elimination called Gauss–Jordan elimination can be used for finding the inverse of a matrix, if it exists. If A is an n × n square matrix, then one can use row reduction to compute its inverse matrix, if it exists. First, the n × n identity matrix is augmented to the right of A, forming an n × 2n block matrix [A | I]
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In mathematics, Jordan decomposition may refer to Hahn decomposition theorem, and the Jordan decomposition of a measure; Jordan normal form of a matrix; Jordan–Chevalley decomposition of a matrix; Deligne–Lusztig theory, and its Jordan decomposition of a character of a finite group of Lie type