TOPICS
Search

Orthogonality Condition

A linear transformation

x_1^'=a_(11)x_1+a_(12)x_2+a_(13)x_3
(1)
x_2^'=a_(21)x_1+a_(22)x_2+a_(23)x_3
(2)
x_3^'=a_(31)x_1+a_(32)x_2+a_(33)x_3,
(3)

is said to be an orthogonal transformation if it satisfies the orthogonality condition

a_(ij)a_(ik)=delta_(jk),
(4)

where Einstein summation has been used and delta_(ij) is the Kronecker delta.

See also

Orthogonal Transformation

Explore with Wolfram|Alpha

References

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

Referenced on Wolfram|Alpha

Orthogonality Condition

Cite this as:

Weisstein, Eric W. "Orthogonality Condition." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/OrthogonalityCondition.html

Subject classifications