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  2. Exchange matrix - Wikipedia

    en.wikipedia.org/wiki/Exchange_matrix

    Premultiplying a matrix by an exchange matrix flips vertically the positions of the former's rows, i.e., () = (). Postmultiplying a matrix by an exchange matrix flips horizontally the positions of the former's columns, i.e., () = ().

  3. Orthogonal array - Wikipedia

    en.wikipedia.org/wiki/Orthogonal_Array

    In mathematics, an orthogonal array (more specifically, a fixed-level orthogonal array) is a "table" (array) whose entries come from a fixed finite set of symbols (for example, {1,2,...,v}), arranged in such a way that there is an integer t so that for every selection of t columns of the table, all ordered t-tuples of the symbols, formed by taking the entries in each row restricted to these ...

  4. Row echelon form - Wikipedia

    en.wikipedia.org/wiki/Row_echelon_form

    Each column containing a leading 1 has zeros in all entries above the leading 1. While a matrix may have several echelon forms, its reduced echelon form is unique. Given a matrix in reduced row echelon form, if one permutes the columns in order to have the leading 1 of the i th row in the i th column, one gets a matrix of the form

  5. Moore–Penrose inverse - Wikipedia

    en.wikipedia.org/wiki/Moore–Penrose_inverse

    For the cases where ⁠ ⁠ has full row or column rank, and the inverse of the correlation matrix (⁠ ⁠ for ⁠ ⁠ with full row rank or ⁠ ⁠ for full column rank) is already known, the pseudoinverse for matrices related to ⁠ ⁠ can be computed by applying the Sherman–Morrison–Woodbury formula to update the inverse of the ...

  6. Row- and column-major order - Wikipedia

    en.wikipedia.org/wiki/Row-_and_column-major_order

    To use column-major order in a row-major environment, or vice versa, for whatever reason, one workaround is to assign non-conventional roles to the indexes (using the first index for the column and the second index for the row), and another is to bypass language syntax by explicitly computing positions in a one-dimensional array.

  7. Gaussian elimination - Wikipedia

    en.wikipedia.org/wiki/Gaussian_elimination

    For each row in a matrix, if the row does not consist of only zeros, then the leftmost nonzero entry is called the leading coefficient (or pivot) of that row. So if two leading coefficients are in the same column, then a row operation of type 3 could be used to make one of those coefficients zero. Then by using the row swapping operation, one ...