enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. 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.

  3. Bareiss algorithm - Wikipedia

    en.wikipedia.org/wiki/Bareiss_algorithm

    In mathematics, the Bareiss algorithm, named after Erwin Bareiss, is an algorithm to calculate the determinant or the echelon form of a matrix with integer entries using only integer arithmetic; any divisions that are performed are guaranteed to be exact (there is no remainder).

  4. Leibniz formula for determinants - Wikipedia

    en.wikipedia.org/wiki/Leibniz_formula_for...

    In algebra, the Leibniz formula, named in honor of Gottfried Leibniz, expresses the determinant of a square matrix in terms of permutations of the matrix elements. If A {\displaystyle A} is an n × n {\displaystyle n\times n} matrix, where a i j {\displaystyle a_{ij}} is the entry in the i {\displaystyle i} -th row and j {\displaystyle j} -th ...

  5. Matrix (mathematics) - Wikipedia

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

    The determinant of this matrix is −1, as the area of the green parallelogram at the right is 1, but the map reverses the orientation, since it turns the counterclockwise orientation of the vectors to a clockwise one. The determinant of a square matrix A (denoted det(A) or | A |) is a number encoding

  6. Jacobi's formula - Wikipedia

    en.wikipedia.org/wiki/Jacobi's_formula

    In matrix calculus, Jacobi's formula expresses the derivative of the determinant of a matrix A in terms of the adjugate of A and the derivative of A. [1]If A is a differentiable map from the real numbers to n × n matrices, then

  7. Rule of Sarrus - Wikipedia

    en.wikipedia.org/wiki/Rule_of_Sarrus

    Rule of Sarrus: The determinant of the three columns on the left is the sum of the products along the down-right diagonals minus the sum of the products along the up-right diagonals. In matrix theory , the rule of Sarrus is a mnemonic device for computing the determinant of a 3 × 3 {\displaystyle 3\times 3} matrix named after the French ...

  8. Xcas - Wikipedia

    en.wikipedia.org/wiki/Xcas

    Calculate average: mean([3, 4, 2]) is 3; Calculate variance: variance([3, 4, 2]) is ⁠ 2 / 3 ⁠ Calculate standard deviation: stddev([3, 4, 2]) is ⁠ √ 6 / 3 ⁠ Calculate determinant of a matrix: det([[1,2], [3,4]]) is −2; Calculate local extrema of a function: extrema(-2*cos(x)-cos(x)^2,x) is [0, π]

  9. Dodgson condensation - Wikipedia

    en.wikipedia.org/wiki/Dodgson_condensation

    Now note that by induction it follows that when applying the Dodgson condensation procedure to a square matrix of order , the matrix in the -th stage of the computation (where the first stage = corresponds to the matrix itself) consists of all the connected minors of order of , where a connected minor is the determinant of a connected sub-block ...