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Instead, the determinant can be evaluated in () operations by forming the LU decomposition = (typically via Gaussian elimination or similar methods), in which case = and the determinants of the triangular matrices and are simply the products of their diagonal entries. (In practical applications of numerical linear algebra, however, explicit ...
In mathematics, Dodgson condensation or method of contractants is a method of computing the determinants of square matrices.It is named for its inventor, Charles Lutwidge Dodgson (better known by his pseudonym, as Lewis Carroll, the popular author), who discovered it in 1866. [1]
Let A be an m × n matrix and k an integer with 0 < k ≤ m, and k ≤ n.A k × k minor of A, also called minor determinant of order k of A or, if m = n, the (n − k) th minor determinant of A (the word "determinant" is often omitted, and the word "degree" is sometimes used instead of "order") is the determinant of a k × k matrix obtained from A by deleting m − k rows and n − k columns.
The determinant of a Cauchy matrix is clearly a rational fraction in the parameters () and (). If the sequences were not injective, the determinant would vanish, and tends to infinity if some x i {\displaystyle x_{i}} tends to y j {\displaystyle y_{j}} .
The determinant of a product of square matrices is the product of the determinants of the factors. The n × n matrices that have an inverse form a group under matrix multiplication, the subgroups of which are called matrix groups .
The determinant of a square Vandermonde matrix is called a Vandermonde polynomial or Vandermonde determinant.Its value is the polynomial = < ()which is non-zero if and only if all are distinct.
It turns out Clint Eastwood really enjoyed Nicholas Hoult's performance in The Great.. When Hoult, 35, appeared on Late Night with Seth Meyers' Thursday, Dec. 19 episode to promote his movie ...
The term secular function has been used for what is now called characteristic polynomial (in some literature the term secular function is still used). The term comes from the fact that the characteristic polynomial was used to calculate secular perturbations (on a time scale of a century, that is, slow compared to annual motion) of planetary ...