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Tagged with linear-algebra uniqueness-theorems
4 questions
16
votes
2
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Definitions of determinant by unique features
A well-known definition of the determinant is:
The determinant is the only function of a vector space of dimension $n$ to its underlying field which is multilinear, alternating and normalized.
See e....
2
votes
1
answer
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What rotations are used as a reduction step in Kenig-Ruiz-Sogge's uniform Sobolev estimate?
I think I have understood the bulk of the paper [KRS], but one of the parts I cannot understand is when the authors reduce Theorem 2.1 (p.332) into Proposition 2.1 (p.335). I can understand all the ...
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1
vote
1
answer
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Reference for (general case) of uniqueness of singular value decomposition (SVD)
My statistics research requires me to understand the non-uniqueness of SVD in the degenerate case of repeated singular values.
I believe that the statements and proofs on this StackExchange posts are ...
1
vote
0
answers
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Infinite dimensional matrix solvability
In order to solve a boundary problem for a conducting hemisphere, the following matrix equation arises (derived from the boundary condition on the curved part of the surface) where we must solve for ...
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