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  2. Duplication and elimination matrices - Wikipedia

    en.wikipedia.org/wiki/Duplication_and...

    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.

  3. Vectorization (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Vectorization_(mathematics)

    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 .

  4. Gaussian elimination - Wikipedia

    en.wikipedia.org/wiki/Gaussian_elimination

    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 ...

  5. LU decomposition - Wikipedia

    en.wikipedia.org/wiki/LU_decomposition

    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).

  6. Row echelon form - Wikipedia

    en.wikipedia.org/wiki/Row_echelon_form

    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

  7. Trump won't kill green energy [Video] - AOL

    www.aol.com/finance/trump-wont-kill-green-energy...

    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.

  8. 1 Social Security Change in 2025 Every Worker Needs to Know - AOL

    www.aol.com/finance/1-social-security-change...

    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 ...

  9. From Gen Z to Boomers: How much money each generation ... - AOL

    www.aol.com/gen-z-boomers-much-money-204351068.html

    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 ...

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