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  2. Jordan matrix - Wikipedia

    en.wikipedia.org/wiki/Jordan_matrix

    This (n 1 + ⋯ + n r) × (n 1 + ⋯ + n r) square matrix, consisting of r diagonal blocks, can be compactly indicated as ,, or (,, …,,), where the i-th Jordan block is J λ i,n i. For example, the matrix = [] is a 10 × 10 Jordan matrix with a 3 × 3 block with eigenvalue 0, two 2 × 2 blocks with eigenvalue the imaginary unit i, and a 3 × ...

  3. Jordan normal form - Wikipedia

    en.wikipedia.org/wiki/Jordan_normal_form

    Example of a matrix in Jordan normal form. All matrix entries not shown are zero. The outlined squares are known as "Jordan blocks". Each Jordan block contains one number λ i on its main diagonal, and 1s directly above the main diagonal. The λ i s are the eigenvalues of the matrix; they need not be distinct.

  4. Matrix decomposition - Wikipedia

    en.wikipedia.org/wiki/Matrix_decomposition

    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.

  5. Examples of Markov chains - Wikipedia

    en.wikipedia.org/wiki/Examples_of_Markov_chains

    The matrix on the left shows how probabilities corresponding to different states can be arranged in matrix form. A state diagram for a simple example is shown in the figure on the right, using a directed graph to picture the state transitions .

  6. Gaussian elimination - Wikipedia

    en.wikipedia.org/wiki/Gaussian_elimination

    Using row operations to convert a matrix into reduced row echelon form is sometimes called Gauss–Jordan elimination. In this case, the term Gaussian elimination refers to the process until it has reached its upper triangular, or (unreduced) row echelon form. For computational reasons, when solving systems of linear equations, it is sometimes ...

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  8. Jordan decomposition - Wikipedia

    en.wikipedia.org/wiki/Jordan_decomposition

    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

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