Search results
Results from the WOW.Com Content Network
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 example, for the 2×2 matrix = [], the half-vectorization is = []. There exist unique matrices transforming the half-vectorization of a matrix to its vectorization and vice versa called, respectively, the duplication matrix and the elimination matrix .
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 ...
For example, we might swap rows to perform partial pivoting, or we might do it to set the pivot element , on the main diagonal to a non-zero number so that we can complete the Gaussian elimination. For our matrix (), we want to set every element below , to zero (where , is the element in the n-th column of the main diagonal).
The reduced row echelon form of a matrix is unique and does not depend on the sequence of elementary row operations used to obtain it. The variant of Gaussian elimination that transforms a matrix to reduced row echelon form is sometimes called Gauss–Jordan elimination. A matrix is in column echelon form if its transpose is in
Trump will probably make a show of eviscerating Biden’s climate plans while rebranding some of them as his own. Markets, in the end, may move in more or less the same direction.
For many older adults, Social Security makes the difference between enjoying a comfortable retirement and struggling to make ends meet. Working in retirement can be a smart way to create financial ...
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 ...