View source for Transposed equations

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

====References====
<table>
<TR><TD valign="top">[a1]</TD> <TD valign="top">  K. Jörgens,   "Lineare Integraloperatoren" , Teubner  (1970)</TD></TR>
<TR><TD valign="top">[a2]</TD> <TD valign="top">  V.I. Smirnov,   "A course of higher mathematics" , '''4''' , Addison-Wesley  (1964)  (Translated from Russian)</TD></TR>
</table>