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In mathematics, especially in linear algebra and matrix theory, the duplication matrix and the elimination matrix are linear transformations used for transforming half-vectorizations of matrices into vectorizations or (respectively) vice versa.
This is the case of the theory of polynomials over an algebraically closed field, where elimination theory may be viewed as the theory of the methods to make quantifier elimination algorithmically effective. Quantifier elimination over the reals is another example, which is fundamental in computational algebraic geometry.
For a symmetric matrix A, the vector vec(A) contains more information than is strictly necessary, since the matrix is completely determined by the symmetry together with the lower triangular portion, that is, the n(n + 1)/2 entries on and below the main diagonal.
Practice theory (or praxeology, theory of social practices) is a body of social theory within anthropology and sociology that explains society and culture as the result of structure and individual agency. Practice theory emerged in the late 20th century and was first outlined in the work of the French sociologist Pierre Bourdieu.
The main theorem of elimination theory is a corollary and a generalization of Macaulay's theory of multivariate resultant. The resultant of n homogeneous polynomials in n variables is the value of a polynomial function of the coefficients, which takes the value zero if and only if the polynomials have a common non-trivial zero over some field ...
But based on market conditions today, that may not be the best approach for 2025 -- not if generating steady income is a big goal of yours. Now if it isn't, you can ignore what I'm saying and keep ...
(Reuters) -U.S. President-elect Donald Trump's transition team is exploring ways to significantly reduce, merge, or even eliminate the top bank regulators in Washington, the Wall Street Journal ...
If Gaussian elimination applied to a square matrix A produces a row echelon matrix B, let d be the product of the scalars by which the determinant has been multiplied, using the above rules. Then the determinant of A is the quotient by d of the product of the elements of the diagonal of B : det ( A ) = ∏ diag ( B ) d . {\displaystyle \det ...