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In mathematics, the determinant is a scalar-valued function of the entries of a square matrix.The determinant of a matrix A is commonly denoted det(A), det A, or | A |.Its value characterizes some properties of the matrix and the linear map represented, on a given basis, by the matrix.
Cramer's rule applies to the case where the coefficient determinant is nonzero. In the 2×2 case, if the coefficient determinant is zero, then the system is inconsistent if the numerator determinants are nonzero, or indeterminate if the numerator determinants are zero.
In vector calculus, the Jacobian matrix (/ dʒ ə ˈ k oʊ b i ə n /, [1] [2] [3] / dʒ ɪ-, j ɪ-/) of a vector-valued function of several variables is the matrix of all its first-order partial derivatives.
Instead, the determinant can be evaluated in () operations by forming the LU decomposition = (typically via Gaussian elimination or similar methods), in which case = and the determinants of the triangular matrices and are simply the products of their diagonal entries. (In practical applications of numerical linear algebra, however, explicit ...
If a statistical procedure ordinarily compares distributions in terms of the determinants of variance-covariance matrices then, in the case of singular matrices, this comparison can be undertaken by using a combination of the ranks of the matrices and their pseudo-determinants, with the matrix of higher rank being counted as "largest" and the pseudo-determinants only being used if the ranks ...
His mother remembered him as a good son with a big heart. “He was an amazing father. He loved his son and had big dreams for him. I remember talking to him and how excited he was for the future ...
CHART #3: SIDE-BY-SIDE COMPARISON OF LEADING REPUBLICAN CANDIDATESÕ HEALTH PLANS By Susan J. Blumenthal, M.D., Jessica B. Rubin, Michelle E. Treseler, Jefferson Lin, and David Mattos*
English: This is the official list of questions (and expected answers) that can be asked on the civics portion of the American naturalization test, revised in January of 2019. While most of these questions are supplied with answers, the ones that ask about specific members of the American government are not.