- #1
hsong9
- 71
- 1
Homework Statement
quaternion q = a + bi + cj + dk
conjugate q* = a - bi - cj - dk
I do not know how I get (q*)* = q
Quaternions, how to prove q^** = q
- Thread starter hsong9
- Start date
-
- Tags
- Quaternions
Click For Summary
SUMMARY
The discussion focuses on proving that the double conjugate of a quaternion, denoted as (q*)*, equals the original quaternion q. The quaternion is defined as q = a + bi + cj + dk, where a, b, c, and d are real numbers. The solution involves applying the definition of the quaternion conjugate, resulting in (q*)* = (a - bi - cj - dk)* = a + bi + cj + dk, confirming that (q*)* indeed equals q.
PREREQUISITES- Understanding of quaternion algebra and notation
- Familiarity with complex numbers and their conjugates
- Basic knowledge of real numbers and their properties
- Ability to manipulate algebraic expressions
- Study quaternion multiplication and its properties
- Explore applications of quaternions in 3D graphics and physics
- Learn about quaternion normalization and its significance
- Investigate the relationship between quaternions and rotation in three-dimensional space
Students studying advanced mathematics, particularly those focusing on linear algebra or 3D computer graphics, as well as anyone interested in the mathematical foundations of quaternions.
Similar threads
- · Replies 3 ·
- · Replies 8 ·
- · Replies 3 ·
- · Replies 8 ·
- · Replies 1 ·
- · Replies 4 ·
- · Replies 3 ·
- · Replies 1 ·