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  2. Symbolab - Wikipedia

    en.wikipedia.org/wiki/Symbolab

    Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]

  3. Matrix exponential - Wikipedia

    en.wikipedia.org/wiki/Matrix_exponential

    For matrix-matrix exponentials, there is a distinction between the left exponential Y X and the right exponential X Y, because the multiplication operator for matrix-to-matrix is not commutative. Moreover, If X is normal and non-singular, then X Y and Y X have the same set of eigenvalues. If X is normal and non-singular, Y is normal, and XY ...

  4. Jacobian matrix and determinant - Wikipedia

    en.wikipedia.org/wiki/Jacobian_matrix_and...

    The Jacobian matrix represents the differential of f at every point where f is differentiable. In detail, if h is a displacement vector represented by a column matrix, the matrix product J(x) ⋅ h is another displacement vector, that is the best linear approximation of the change of f in a neighborhood of x, if f(x) is differentiable at x.

  5. 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 ...

  6. Determinant - Wikipedia

    en.wikipedia.org/wiki/Determinant

    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. In particular, the determinant is nonzero if and only if the matrix is invertible and the corresponding linear map is an isomorphism.

  7. Cramer's rule - Wikipedia

    en.wikipedia.org/wiki/Cramer's_rule

    where is the matrix formed by replacing the i-th column of A by the column vector b. A more general version of Cramer's rule [13] considers the matrix equation = where the n × n matrix A has a nonzero determinant, and X, B are n × m matrices.

  8. Jacobi method - Wikipedia

    en.wikipedia.org/wiki/Jacobi_method

    Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi.

  9. Matrix multiplication - Wikipedia

    en.wikipedia.org/wiki/Matrix_multiplication

    In mathematics, specifically in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the ...