enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Adjugate matrix - Wikipedia

    en.wikipedia.org/wiki/Adjugate_matrix

    In linear algebra, the adjugate or classical adjoint of a square matrix A, adj(A), is the transpose of its cofactor matrix. [ 1 ] [ 2 ] It is occasionally known as adjunct matrix , [ 3 ] [ 4 ] or "adjoint", [ 5 ] though that normally refers to a different concept, the adjoint operator which for a matrix is the conjugate transpose .

  3. Conjugate transpose - Wikipedia

    en.wikipedia.org/wiki/Conjugate_transpose

    The conjugate transpose "adjoint" matrix should not be confused with the adjugate, ⁡ (), which is also sometimes called adjoint. The conjugate transpose of a matrix A {\displaystyle \mathbf {A} } with real entries reduces to the transpose of A {\displaystyle \mathbf {A} } , as the conjugate of a real number is the number itself.

  4. Hermitian adjoint - Wikipedia

    en.wikipedia.org/wiki/Hermitian_adjoint

    In mathematics, specifically in operator theory, each linear operator on an inner product space defines a Hermitian adjoint (or adjoint) operator on that space according to the rule A x , y = x , A ∗ y , {\displaystyle \langle Ax,y\rangle =\langle x,A^{*}y\rangle ,}

  5. Adjoint - Wikipedia

    en.wikipedia.org/wiki/Adjoint

    Several of these share a similar formalism: if A is adjoint to B, then there is typically some formula of the type (Ax, y) = (x, By). Specifically, adjoint or adjunction may mean: Adjoint of a linear map, also called its transpose in case of matrices; Hermitian adjoint (adjoint of a linear operator) in functional analysis

  6. Adjoint functors - Wikipedia

    en.wikipedia.org/wiki/Adjoint_functors

    The definitions via universal morphisms are easy to state, and require minimal verifications when constructing an adjoint functor or proving two functors are adjoint. They are also the most analogous to our intuition involving optimizations. The definition via hom-sets makes symmetry the most apparent, and is the reason for using the word adjoint.

  7. Laplace operator - Wikipedia

    en.wikipedia.org/wiki/Laplace_operator

    As a second-order differential operator, the Laplace operator maps C k functions to C k−2 functions for k ≥ 2.It is a linear operator Δ : C k (R n) → C k−2 (R n), or more generally, an operator Δ : C k (Ω) → C k−2 (Ω) for any open set Ω ⊆ R n.

  8. Complex conjugate - Wikipedia

    en.wikipedia.org/wiki/Complex_conjugate

    Geometric representation (Argand diagram) of and its conjugate ¯ in the complex plane.The complex conjugate is found by reflecting across the real axis.. In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign.

  9. Jacobian matrix and determinant - Wikipedia

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

    The determinant is ρ 2 sin φ. Since dV = dx dy dz is the volume for a rectangular differential volume element (because the volume of a rectangular prism is the product of its sides), we can interpret dV = ρ 2 sin φ dρ dφ dθ as the volume of the spherical differential volume element.