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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.
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.
Row echelon form — a matrix in this form is the result of applying the forward elimination procedure to a matrix (as used in Gaussian elimination). Wronskian — the determinant of a matrix of functions and their derivatives such that row n is the (n−1) th derivative of row one.
This lemma generalizes one of the Finsler's lemma variants by including an extra matrix C and an extra constraint involving this extra matrix. It is interesting to note that if the strict inequalities are changed to non-strict inequalities, the equivalence does not hold anymore: only the second statement imply the first statement.
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 ...
Americans in all age brackets are making far less money than they think they need to be successful, according to new research. A "Secret to Success" study published Tuesday by Empower, a financial ...
Duplication, or doubling, multiplication by 2; Duplication matrix, a linear transformation dealing with half-vectorization; Doubling the cube, a problem in geometry also known as duplication of the cube; A type of multiplication theorem called the Legendre duplication formula or simply "duplication formula"
A key piece of evidence against Mr Hakamata were red-stained clothes found in a miso tank at his workplace. They were recovered a year and two months after the murders and the prosecution said ...