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According to the first condition, this is a necessary condition, but not a sufficient one. Therefore, the two definitions are not equivalent. Presumably it should also include the fact that the summation should equal
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Actually, no, hang on. That alternative definition is dangerous. Is there anything to prevent these matrices having zero-valued elements? If not, then the alternative definition will be meaningless.
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https://web.archive.org/web/20110722132459/http://mdmc.chonbuk.ac.kr/english/images/Jacket%20matrix%20and%20its%20fast%20algorithm%20for%20wireless%20signal%20processing.pdf
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it's saying that each element of the conjugate transpose is the inverse of the corresponding element of the original matrix. This is clearly not the case in the example.
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I see someone's now removed the alternative definition from the lead. If that's because it's wrong, it also needs removing from the "Properties" section.
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Does the jacket matrix work over fields in general, or only over the specific examples mentioned? If it's the former, all that need be said is:
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When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
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http://mdmc.chonbuk.ac.kr/english/images/Jacket%20matrix%20and%20its%20fast%20algorithm%20for%20wireless%20signal%20processing.pdf
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Maybe I'm being slow, but I'm not sure how that validates the "discrepancy" I think exists above! If I understand the notation:
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A possible compromise is to simply remove the definitions. What purpose do they serve on a page about jacket matrices?
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to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
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Right, I see someone's fixed the problem I mentioned above. However, the "different form" also worries me:
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These currently don't agree (because of the overall scaling by 1/4). Should the property actually read:
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If you have discovered URLs which were erroneously considered dead by the bot, you can report them with
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on
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1063:{\displaystyle \sum _{i=1}^{n}{a_{u,i} \over a_{v,i}}=0{\text{ for }}u,v\in \{1,\dots ,n\},\ u\neq v.}
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https://web.archive.org/web/20110722132439/http://mdmc.chonbuk.ac.kr/english/download/report%201.pdf
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before doing mass systematic removals. This message is updated dynamically through the template
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Actually, nevermind! I've just realised that's it's self-evident what the summation is when
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If you found an error with any archives or the URLs themselves, you can fix them with
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whose entries are from a real field, a complex field or a finite field.
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However, the defining property of a jacket matrix is given by:
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for additional information. I made the following changes:
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http://mdmc.chonbuk.ac.kr/english/download/report%201.pdf
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593:{\displaystyle \ A^{\mathrm {*} }=(a_{ji}^{-1})}
1232:Constraints for orthogonal and unitary matrices
1575:This message was posted before February 2018.
1464:{\displaystyle \sum _{i=1}^{n}|a_{u,i}|^{2}=1}
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819:{\displaystyle A^{*}A=AA^{*}=I_{n}.\,}
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1532:Hello fellow Wikipedians,
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1309:{\displaystyle UU^{*}=I}
1273:{\displaystyle QQ^{T}=I}
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169:project's priority scale
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1638:Report bug
1621:this tool
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1520:Oli Filth
1501:Oli Filth
1491:Oli Filth
1320:, hence:
1224:Oli Filth
1187:Oli Filth
1176:Oli Filth
1098:Oli Filth
1088:Oli Filth
917:Oli Filth
675:Oli Filth
1627:Cheers.—
756:It does
189:Example?
28:deletion
1541:my edit
167:on the
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502:−
494:−
479:−
464:−
437:−
410:−
354:−
316:−
308:−
293:−
285:−
265:−
252:−
1640:)
1636:(
1623:.
1616:.
1459:1
1456:=
1451:2
1446:|
1439:i
1436:,
1433:u
1429:a
1424:|
1418:n
1413:1
1410:=
1407:i
1376:1
1373:=
1368:2
1363:i
1360:,
1357:u
1353:a
1347:n
1342:1
1339:=
1336:i
1304:I
1301:=
1292:U
1288:U
1268:I
1265:=
1260:T
1256:Q
1252:Q
1219:"
1215:"
1207:"
1203:"
1162:1
1159:=
1152:i
1149:,
1146:v
1142:a
1136:i
1133:,
1130:u
1126:a
1113:v
1109:u
1084:v
1082:=
1080:u
1076:n
1058:.
1055:v
1049:u
1044:,
1041:}
1038:n
1035:,
1029:,
1026:1
1023:{
1017:v
1014:,
1011:u
1003:0
1000:=
993:i
990:,
987:v
983:a
977:i
974:,
971:u
967:a
959:n
954:1
951:=
948:i
899:)
894:1
886:i
883:j
879:a
875:(
872:=
861:A
834:(
812:.
807:n
803:I
799:=
790:A
786:A
783:=
780:A
771:A
738:.
733:n
729:I
725:n
722:=
713:A
709:A
706:=
703:A
694:A
658:)
653:1
645:i
642:j
638:a
634:(
631:k
628:=
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588:)
583:1
575:i
572:j
568:a
564:(
561:=
550:A
521:.
517:]
510:1
505:1
497:1
489:1
482:1
472:2
469:1
457:2
454:1
447:1
440:1
430:2
427:1
418:2
415:1
405:1
398:1
393:1
388:1
383:1
376:[
370:4
367:1
362:=
357:1
349:4
345:J
335:,
331:]
324:1
319:1
311:1
303:1
296:1
288:2
280:2
275:1
268:1
260:2
255:2
247:1
240:1
235:1
230:1
225:1
218:[
214:=
209:4
205:J
171:.
70::
38:.
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