Normal equation
From Encyclopedia of Mathematics
normalized equation
The equation of a line in a plane of the form
 |
where 
and 
are rectangular Cartesian coordinates in the plane, 
and 
are the coordinates of the unit vector 
perpendicular to the line, and 
is the distance of the coordinate origin from the line. An equation of a line of the form
 |
reduces to normal form after multiplication by the normalizing factor 
of absolute value 
and of sign opposite to that of 
(if 
, the sign of 
is arbitrary).
Similarly, the equation of a plane
 |
reduces to the normal form
 |
where 
, 
and 
are the direction cosines of a vector perpendicular to the plane, after multiplication by the normalizing factor 
of absolute value 
and of sign opposite to that of 
.
How to Cite This Entry:
Normal equation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Normal_equation&oldid=32443
Normal equation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Normal_equation&oldid=32443
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article