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  2. Minor (linear algebra) - Wikipedia

    en.wikipedia.org/wiki/Minor_(linear_algebra)

    If the matrix that corresponds to a principal minor is a square upper-left submatrix of the larger matrix (i.e., it consists of matrix elements in rows and columns from 1 to k, also known as a leading principal submatrix), then the principal minor is called a leading principal minor (of order k) or corner (principal) minor (of order k). [3]

  3. LU decomposition - Wikipedia

    en.wikipedia.org/wiki/LU_decomposition

    7.4 MATLAB code example. 8 See ... columns are linearly independent and at least one leading principal minor is ... is -1. Matrix formulae to calculate rows and ...

  4. Main diagonal - Wikipedia

    en.wikipedia.org/wiki/Main_diagonal

    For a square matrix, the diagonal (or main diagonal or principal diagonal) is the diagonal line of entries running from the top-left corner to the bottom-right corner. [1] [2] [3] For a matrix with row index specified by and column index specified by , these would be entries with =.

  5. Hurwitz determinant - Wikipedia

    en.wikipedia.org/wiki/Hurwitz_determinant

    The i-th Hurwitz determinant is the i-th leading principal minor (minor is a determinant) of the above Hurwitz matrix H. There are n Hurwitz determinants for a characteristic polynomial of degree n .

  6. Hessian matrix - Wikipedia

    en.wikipedia.org/wiki/Hessian_matrix

    Specifically, sign conditions are imposed on the sequence of leading principal minors (determinants of upper-left-justified sub-matrices) of the bordered Hessian, for which the first leading principal minors are neglected, the smallest minor consisting of the truncated first + rows and columns, the next consisting of the truncated first + rows ...

  7. Routh–Hurwitz stability criterion - Wikipedia

    en.wikipedia.org/wiki/Routh–Hurwitz_stability...

    Compute the Sylvester matrix associated to and (). Rearrange each row in such a way that an odd row and the following one have the same number of leading zeros. Compute each principal minor of that matrix. If at least one of the minors is negative (or zero), then the polynomial f is not stable.

  8. P-matrix - Wikipedia

    en.wikipedia.org/wiki/P-matrix

    In mathematics, a P-matrix is a complex square matrix with every principal minor is positive. A closely related class is that of P 0 {\displaystyle P_{0}} -matrices, which are the closure of the class of P -matrices, with every principal minor ≥ {\displaystyle \geq } 0.

  9. 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

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