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See also my list of links to my other RG documents:
https://www.researchgate.net/publication/325464379_Links_to_my_RG_pages
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Original question posted on May 16, 2018: Are there extensions of the concept of angles between two planes? The concept of angle between two planes in the ordinary 3-dimensional space is well-known. Are there extensions of this concept to angles between two vector subspaces of a vector space?
Improved question posted on May 17, 2018.
I have posted a list of references about angles between two vector subspaces on the following Web page:
https://www.researchgate.net/project/Study-of-angles-between-vector-subspaces
My improved question is in the following two parts:
Part 1: Are there references that are not on this list?
Part 2: Which of these references is the best?
I will add to my list any new references and any good comment about these references, with full credit to the first who finds it.
Dear Jean-Claude Evard,
Sure, the generalization tackled by many authors.
One of the exciting articles is
(A Formula for Angles between Subspaces of Inner Product Spaces)
https://www.emis.de/journals/BAG/vol.46/no.2/b46h2gun.pdf
Best regards
Comments posted on May 16, 2018
I thank Issam Kaddoura a lot for his above answer to my question of this morning with his reference to the following article:
A Formula for Angles between Subspaces of Inner Product Spaces
Hendra Gunawan
https://www.researchgate.net/profile/Hendra_Gunawan2
Oki Neswan
https://www.researchgate.net/profile/Oki_Neswan
and Wono Setya-Budhi
https://www.researchgate.net/profile/Wono_Setya_Budhi
Beitr¨age zur Algebra und Geometrie
Contributions to Algebra and Geometry
Volume 46, issue 2, pages 311—320
October 18, 2005
https://www.emis.de/
https://www.emis.de/journals/BAG/
https://www.emis.de/journals/BAG/vol.46/no.2/2.html
https://www.emis.de/journals/BAG/vol.46/no.2/b46h2gun.pdf
https://www.researchgate.net/publication/265928213_A_Formula_for_Angles_between_Subspaces_of_Inner_Product_Spaces
I have posted a new project about angles between vector subspaces on the following Web page:
https://www.researchgate.net/project/Study-of-angles-between-vector-subspaces
I have added the above reference to the list of references posted on this new Web page, with full credit to Issam.
Many mathematicians will be very interested in any new references on angles between subspaces that anyone could find and that are currently missing on my list.
I will be happy to add every new reference to my new Web page with full credit to the first who finds the new reference.
I thank Issam again a lot for his reference.
With best regards, Jean-Claude
yes, there is such an extension.
a very detailed discussion of this can be found in the following book, in the chapter titled Norms, Inner products and Orthogonality.
" Matrix analysis and Applied Linear Algebra ", Author- Carl.D.Meyer , SIAM.
Comment posted on May 21, 2018
I thank a lot Debopam Ghosh for his reference to the book of Carl Meyer and for his comment. This reference was impossible to find by Internet search, because there is nothing in the title of Carl’s book saying that there is an important section on angles between subspaces, and there are hundreds of books of matrix theory and linear algebra without such a section. Nobody can check hundreds of books. I have added Debopam’s reference to the list of references posted in my research project about angles between subspace, and I have given full credit to Debopam for his reference.
With best regards, Jean-Claude
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