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  2. QR decomposition - Wikipedia

    en.wikipedia.org/wiki/QR_decomposition

    More generally, we can factor a complex m×n matrix A, with m ≥ n, as the product of an m×m unitary matrix Q and an m×n upper triangular matrix R.As the bottom (m−n) rows of an m×n upper triangular matrix consist entirely of zeroes, it is often useful to partition R, or both R and Q:

  3. QR algorithm - Wikipedia

    en.wikipedia.org/wiki/QR_algorithm

    Instead, the QR algorithm works with a complete basis of vectors, using QR decomposition to renormalize (and orthogonalize). For a symmetric matrix A , upon convergence, AQ = QΛ , where Λ is the diagonal matrix of eigenvalues to which A converged, and where Q is a composite of all the orthogonal similarity transforms required to get there.

  4. Template:QR code - Wikipedia

    en.wikipedia.org/wiki/Template:QR_code

    If used without parameters then the current page the template is on is linked to a QR image for that page.. 1 - The first parameter provides a Wikipedia article name to provide a link to the article followed by a link to the QR code image page (service provided by Google).

  5. RRQR factorization - Wikipedia

    en.wikipedia.org/wiki/RRQR_factorization

    An RRQR factorization or rank-revealing QR factorization is a matrix decomposition algorithm based on the QR factorization which can be used to determine the rank of a matrix. [1] The singular value decomposition can be used to generate an RRQR, but it is not an efficient method to do so. [2] An RRQR implementation is available in MATLAB. [3]

  6. Matrix decomposition - Wikipedia

    en.wikipedia.org/wiki/Matrix_decomposition

    Also known as: UTV decomposition, ULV decomposition, URV decomposition. Applicable to: m-by-n matrix A. Decomposition: =, where T is a triangular matrix, and U and V are unitary matrices. Comment: Similar to the singular value decomposition and to the Schur decomposition.

  7. Eigendecomposition of a matrix - Wikipedia

    en.wikipedia.org/wiki/Eigendecomposition_of_a_matrix

    In the QR algorithm for a Hermitian matrix (or any normal matrix), the orthonormal eigenvectors are obtained as a product of the Q matrices from the steps in the algorithm. [11] For more general matrices, the QR algorithm yields the Schur decomposition first, from which the eigenvectors can be obtained by a backsubstitution procedure. [ 13 ] )