Transposed equations

The transposed equations of a linear algebraic system are the linear equations with the transposed matrix as coefficient matrix.

In the case of linear integral equations (cf. Integral equation), transposed equations are equations with kernels $K(x,y)$ and $K(y,x)$.

Transposed equations are also called adjoint equations or associated equations.

#### Comments[edit]

The transposed equation of an integral equation plays an important role in the Fredholm alternative.

#### References[edit]

[a1] |  K. Jörgens, "Lineare Integraloperatoren" , Teubner (1970)

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[a2] |  V.I. Smirnov, "A course of higher mathematics" , 4 , Addison-Wesley (1964) (Translated from Russian)