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1. • CommentRowNumber1.
   • CommentAuthorTobyBartels
   • CommentTimeJan 16th 2017
   • (edited Jan 18th 2017)
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexTo make sense of this in my mind as a general concept, I have written [[semidefinite element]]. This gives a general context in which to define ‘positive definite’, ‘negative semidefinite’, ‘indefinite’ etc. (This seems the safest page title, as the least likely to have any conflicts. I\'ve also put in a lot of redirects, but possibly some of these will have to go elsewhere; [[definite]] seems the most dangerous.)

   To make sense of this in my mind as a general concept, I have written semidefinite element. This gives a general context in which to define ‘positive definite’, ‘negative semidefinite’, ‘indefinite’ etc.

   (This seems the safest page title, as the least likely to have any conflicts. I've also put in a lot of redirects, but possibly some of these will have to go elsewhere; definite seems the most dangerous.)

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeJan 16th 2017
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexNeat. It's not quite clear to me how you're getting the case of bilinear forms: are you regarding them as function sets as in the paragraph two above?

   Neat. It’s not quite clear to me how you’re getting the case of bilinear forms: are you regarding them as function sets as in the paragraph two above?

3. • CommentRowNumber3.
   • CommentAuthorTobyBartels
   • CommentTimeJan 17th 2017
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexNo, and the definitions aren\'t spelt out on [[semidefinite element]], since they\'re spelt out at [[inner product space]], so I just referenced that.

   No, and the definitions aren't spelt out on semidefinite element, since they're spelt out at inner product space, so I just referenced that.

4. • CommentRowNumber4.
   • CommentAuthorMike Shulman
   • CommentTimeJan 18th 2017
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexI don't understand. The page [[inner product space]] defines words like "semidefinite" directly. But the page [[semidefinite element]] defines those same words in terms of a structure $\le, \#, 0$. What I seek is a definition of the structure $\le,\#,0$ that causes the definitions of "semidefinite" etc. given at [[semidefinite element]] to coincide with those given at [[inner product space]].

   I don’t understand. The page inner product space defines words like “semidefinite” directly. But the page semidefinite element defines those same words in terms of a structure $\le, \#, 0$. What I seek is a definition of the structure $\le,\#,0$ that causes the definitions of “semidefinite” etc. given at semidefinite element to coincide with those given at inner product space.

5. • CommentRowNumber5.
   • CommentAuthorTobyBartels
   • CommentTimeJan 18th 2017
   • (edited Jan 18th 2017)
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexSymmetric bilinear forms (or more generally conjugate-symmetric sesquilinear forms) form an abelian group under addition (this much treats them as forming [a subset of] a function set), so if you know what ‘semidefinite’ and ‘nonsingular’ (aka ‘nondegenerate’) mean, then you know what $\leq$, $#$, and $0$ are. Perhaps I should spell that out more. ETA: That is the reason for the comment ‘The obvious additive group structure is compatible (which explains what $\leq$, $#$, and $0$ mean)’.

   Symmetric bilinear forms (or more generally conjugate-symmetric sesquilinear forms) form an abelian group under addition (this much treats them as forming [a subset of] a function set), so if you know what ‘semidefinite’ and ‘nonsingular’ (aka ‘nondegenerate’) mean, then you know what $\leq$, $#$, and $0$ are. Perhaps I should spell that out more.

   ETA: That is the reason for the comment ‘The obvious additive group structure is compatible (which explains what $\leq$, $#$, and $0$ mean)’.

6. • CommentRowNumber6.
   • CommentAuthorTobyBartels
   • CommentTimeJan 18th 2017
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexI made a mistake in \#1, saying that [[indefinite]] was the most dangerous redirect; I forgot that I had been so bold as to include [[definite]]! (I now fixed \#1.)

   I made a mistake in #1, saying that indefinite was the most dangerous redirect; I forgot that I had been so bold as to include definite! (I now fixed #1.)

7. • CommentRowNumber7.
   • CommentAuthorMike Shulman
   • CommentTimeJan 19th 2017
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexSpelling it out would help me.

   Spelling it out would help me.