# Transposed equations

From Encyclopedia of Mathematics

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

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

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

**How to Cite This Entry:**

Transposed equations.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Transposed_equations&oldid=34732