Adjoint equation

adjoint equation

An equation of the form x₀ = 𝗟^Tx₁, in which the linear operator 𝗟^T is the adjoint of the matrix operator 𝗟 that satisfies (𝗟^Tx₁,x₀) = (x₁,𝗟x₀), where x₀ and x₁ are vectors and (,) represents an inner product.

If (,) is the standard dot product (Euclidean inner product) then 𝗟^T is simply the transpose of 𝗟.
See adjoint sensitivity, adjoint model, tangent linear equation.

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An equation of the form x₀ = 𝗟^Tx₁, in which the linear operator 𝗟^T is the adjoint of the matrix operator 𝗟 that satisfies (𝗟^Tx₁,x₀) = (x₁,𝗟x₀), where x₀ and x₁ are vectors and (,) represents an inner product.