Namespaces
Variants
Actions

Difference between revisions of "Transposed equations"

From Encyclopedia of Mathematics
Jump to: navigation, search
(Importing text file)
 
(LaTeX)
 
Line 1: Line 1:
The transposed equations of a linear algebraic system are the linear equations with the [[Transposed matrix|transposed matrix]] as coefficient matrix.
+
{{TEX|done}}
  
In the case of linear integral equations (cf. [[Integral equation|Integral equation]]), transposed equations are equations with kernels <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/t/t093/t093940/t0939401.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/t/t093/t093940/t0939402.png" />.
+
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.
 
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 [[Fredholm alternative|Fredholm alternative]].
+
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=34732