- #1
hsong9
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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
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- Tags
- Quaternions
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Homework Help Overview
The discussion revolves around proving a property of quaternions, specifically that the double conjugate of a quaternion \( q \) equals \( q \) itself. The original poster presents the quaternion in its standard form and expresses uncertainty about how to demonstrate this property.
Discussion Character
- Conceptual clarification, Mathematical reasoning
Approaches and Questions Raised
- Participants discuss the nature of the components of the quaternion, questioning whether \( a, b, c, \) and \( d \) are real numbers. They suggest taking the double conjugate as a method to prove the property.
Discussion Status
Some participants have provided guidance on the approach to take, specifically mentioning the process of applying the conjugate operation twice. There is an indication that the discussion is moving towards a resolution, but no explicit consensus has been reached.
Contextual Notes
Participants are operating under the assumption that the components of the quaternion are real numbers, which is a typical constraint in quaternion discussions. The original poster's uncertainty about the proof indicates a need for further exploration of the properties of quaternions.
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