info prev up next book cdrom email home

Orthogonality Condition

A linear transformation

$\displaystyle x_1'$ $\textstyle =$ $\displaystyle a_{11}x_1+a_{12}x_2+x_{13}x_3$  
$\displaystyle x_2'$ $\textstyle =$ $\displaystyle a_{21}x_1+a_{22}x_2+a_{23}x_3$  
$\displaystyle x_3'$ $\textstyle =$ $\displaystyle a_{31}x_1+a_{32}x_2+a_{33}x_3,$  

is said to be an Orthogonal Transformation if it satisfies the orthogonality condition

a_{ij}a_{ik} = \delta_{jk},

where Einstein Summation has been used and $\delta_{ij}$ is the Kronecker Delta.

See also Orthogonal Transformation


Goldstein, H. ``Orthogonal Transformations.'' §4-2 in Classical Mechanics, 2nd ed. Reading, MA: Addison-Wesley, 132-137, 1980.

© 1996-9 Eric W. Weisstein