Difference between revisions of "Transposed equations"
From Encyclopedia of Mathematics
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| − | In the case of linear integral equations (cf. [[ | + | The transposed equations of a linear algebraic system are the linear equations with the [[transposed matrix]] as coefficient matrix. |
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| + | 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. | Transposed equations are also called adjoint equations or associated equations. | ||
====Comments==== | ====Comments==== | ||
| − | The transposed equation of an integral equation plays an important role in the [[ | + | The transposed equation of an integral equation plays an important role in the [[Fredholm alternative]]. |
====References==== | ====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> | + | <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> | ||
Latest revision as of 20:32, 21 November 2014
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=12035
Transposed equations. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Transposed_equations&oldid=12035