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1070:{\displaystyle \mathbf {a} \times \mathbf {b} ={\begin{bmatrix}a_{x}\\a_{y}\\a_{z}\end{bmatrix}}\times {\begin{bmatrix}b_{x}\\b_{y}\\b_{z}\end{bmatrix}}={\begin{bmatrix}0&-a_{z}&a_{y}\\a_{z}&0&-a_{x}\\-a_{y}&a_{x}&0\end{bmatrix}}{\begin{bmatrix}b_{x}\\b_{y}\\b_{z}\end{bmatrix}}=\mathbf {\hat {a}} \mathbf {b} }
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is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in
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are denoted with hat notation. For instance, see the time-independent Schrödinger equation, where the
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indicates an observable estimate (the residuals) of an unobservable quantity called
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729:{\displaystyle \mathbf {a} \times \mathbf {b} =\mathbf {\hat {a}} \mathbf {b} }
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422:{\displaystyle {\hat {y}}_{i}={\hat {\beta }}_{0}+{\hat {\beta }}_{1}x_{i}}
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1126:(pronounced "v-hat"). This is especially common in physics context.
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Another example of the hat operator denoting an estimator occurs in
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278:{\displaystyle y_{i}=\beta _{0}+\beta _{1}x_{i}+\varepsilon _{i}}
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Applied
Mathematics for Physical Chemistry: Third Edition
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or an estimated value. For example, in the context of
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Pages displaying wikidata descriptions as a fallback
644:{\displaystyle {\hat {\mathbf {y} }}=H\mathbf {y} .}
494:{\displaystyle \sum _{i}(y_{i}-{\hat {y}}_{i})^{2}}
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Help:Displaying a formula § Special characters
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683:and transforms it into its equivalent matrix.
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599:of response variable to the predicted values
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58:introducing citations to additional sources
1286: – Algebra of exterior/ wedge products
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145:(ˆ), called a "hat", is used to denote an
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1359:. Waveland Press. Page 124, Footnote 1.
48:Relevant discussion may be found on the
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1268:{\displaystyle {\hat {H}}\psi =E\psi }
1119:{\displaystyle {\hat {\mathbf {v} }}}
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175:{\displaystyle {\hat {\varepsilon }}}
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1091:In mathematics, a unit vector in a
570:{\displaystyle {\hat {\beta }}_{1}}
534:{\displaystyle {\hat {\beta }}_{0}}
1400:. You can help Knowledge (XXG) by
1298: – signal filtering technique
739:For example, in three dimensions,
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1353:Barrante, James R. (2016-02-10).
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1290:Glossary of mathematical symbols
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667:operator is to represent the
595:projects the observed values
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1158:is traditionally denoted by
679:. The hat operator takes a
312:and dependent variable data
195:{\displaystyle \varepsilon }
153:, the "hat" over the letter
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1225:{\displaystyle {\hat {H}}}
1180:{\displaystyle {\hat {f}}}
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501:is commonly minimized via
202:(the statistical errors).
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207:simple linear regression
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1396:-related article is a
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1195:In quantum mechanics,
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16:Mathematical notation
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54:improve this article
1328:Weisstein, Eric W.
1093:normed vector space
129:with various uses.
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69:"Hat notation"
52:. Please help
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669:cross product
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655:Cross product
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71: –
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65:Find sources:
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43:single source
39:This article
37:
33:
28:
27:
22:
1402:expanding it
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1337:. Retrieved
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661:screw theory
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1203:is denoted
1087:Unit vector
1081:Unit vector
1441:Categories
1339:2024-08-29
1312:References
1305:Circumflex
587:hat matrix
581:Hat matrix
143:circumflex
139:statistics
123:circumflex
80:newspapers
1263:ψ
1254:ψ
1248:^
1217:^
1197:operators
1172:^
1111:^
1057:^
956:−
939:−
893:−
820:×
755:×
716:^
699:×
622:^
556:^
553:β
520:^
517:β
470:^
460:−
438:∑
398:^
395:β
376:^
373:β
354:^
267:ε
244:β
231:β
190:ε
167:^
164:ε
147:estimator
121:A "hat" (
50:talk page
1278:See also
1191:Operator
110:May 2024
1394:algebra
94:scholar
1363:
681:vector
677:matrix
429:where
96:
89:
82:
75:
67:
1392:This
1330:"Hat"
101:JSTOR
87:books
1398:stub
1361:ISBN
1134:The
541:and
141:, a
73:news
665:hat
659:In
603::
137:In
56:by
1443::
1332:.
1320:^
1232:.
1187:.
1429:e
1422:t
1415:v
1404:.
1369:.
1342:.
1260:E
1257:=
1245:H
1214:H
1169:f
1146:f
1107:v
1064:b
1054:a
1048:=
1043:]
1035:z
1031:b
1021:y
1017:b
1007:x
1003:b
996:[
989:]
983:0
976:x
972:a
964:y
960:a
947:x
943:a
934:0
927:z
923:a
913:y
909:a
901:z
897:a
888:0
882:[
877:=
872:]
864:z
860:b
850:y
846:b
836:x
832:b
825:[
815:]
807:z
803:a
793:y
789:a
779:x
775:a
768:[
763:=
759:b
751:a
723:b
713:a
707:=
703:b
695:a
639:.
635:y
631:H
628:=
618:y
601:ŷ
597:y
593:H
563:1
527:0
487:2
483:)
477:i
467:y
455:i
451:y
447:(
442:i
415:i
411:x
405:1
388:+
383:0
366:=
361:i
351:y
325:i
321:y
298:i
294:x
271:i
263:+
258:i
254:x
248:1
240:+
235:0
227:=
222:i
218:y
112:)
108:(
98:·
91:·
84:·
77:·
60:.
46:.
23:.
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