Talk:Chatbot math/Bard/24.02/Unitary Transformation & Matrix Symmetry

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Comments by Guy vandegrift

Unitary Transformation & Matrix Symmetry

• See the full chat at Chatbot math/Bard/24.02/Unitary Transformation & Matrix Symmetry

This chat with Bard has me convinced that discussions between Bard and WMF editors could be mutually beneficial.

Key points in this chat:

• I was working on a physics project, where it was obvious that a symmetric matrix (a_ij=a_ji) maintained that symmetry under a rotational transformation (a'=R^TaR.) I assumed this would be valid for any unitary transformation and any nxn symmetric matrix. Just to be sure, I decided to do a "quick" check using Bard. It turned out to be far from quick.
• To my surprise Bard claimed that all symmetric matrices do not remain symmetric under a unitary transformation. After a few exchanges, I discovered that Bard and I had a serious misunderstanding as to the meaning of an nxn matrix. My question and Bard's answer can be found at the following link:

#I am confused. A has nine elements. But the transformed matrix, B, has 27 elements. I though B would have nine elements.

• Bard offered to sort things out, so I took Bard up on the offer. I soon reached a point of diminishing returns, that caused me to ask a crucial question; Bards answer can be found by clicking the following link:

#Just out of curiosity, was this conversation useful to you? If so, I will make it a habit to discuss a calculation where you made a mistake.

• Bard reiterated its "interest" in getting help from me (and presumably other WMF editors) in its response to my closing message to Bard:

#I will post this on Wikiversity and leave a note on a Wikipedia talk page. Don't worry, this problem will get solved. Goodbye, for now. I will sign off as I would on Wikipedia/Wikiversity --user:Guy vandegrift

This quote is from Bard's closing remark:

“ I'm glad you plan to share this on Wikiversity and Wikipedia, as open discussion and collaborative problem-solving are essential for knowledge advancement. While I cannot directly participate in those platforms, I would be interested in seeing any insights or solutions derived from the discussion. ”

I never told Bard what Wikipedia/Wikiversity is, so Bard already knew that it was about "open discussion and collaborative problem-solving" (as Bard put it.) I also liked it that Bard addressed my by my username. Guy vandegrift (discuss • contribs) 23:23, 6 February 2024 (UTC)