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1979幎 æ¥æ¬ã§ã¯1970幎代åŸåããããã€ãã®å°èŠæš¡ãªã¡ãŒã«ãŒãèããããããã€ãªãã¢ã»ã¢ã¹ç€Ÿãã¹ããŒã®è§£æŸåãã¬ãŒããæ¹è¯ããåºå®åŒããŒããã€ã³ãã£ã³ã°ãæã€ãMOSS snowstickãã®è²©å£²ãéå§ãããã¯ã¹ããŒããŒãã®äœ¿çšãåæãšããäžçã§åããŠåºå®åŒãã€ã³ãã£ã³ã°ãæ¡çšãããã®ã§ããããMOSS SNOWBOARDãã¯çŸåããäžççå€åã¡ãŒã«ãŒãšããŠç¥ãããŠããã
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| false | false | false |
https://ja.wikipedia.org/wiki/%E6%A1%9C%E6%9C%A8%E7%94%BA%E9%A7%85
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7,712 |
ç察称
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åç幟äœåŠã«ããã幟äœåŠç察象ãç察称(ãã
ãããããããè±: radial symmetric; æŸå°å¯Ÿç§°)ãããã¯å転äžå€(ãããŠããµãžããè±: rotational invariant)ã§ãããšã¯ããã®å¯Ÿè±¡ããä»»æã®ãåè»¢å€æ(ããªãã¡ã察象ã®äžå¿ãéãä»»æã®è»žã«å¯Ÿããä»»æè§åºŠã®å転)ã«å¯ŸããŠäžå€ãšãªãããšããããåŸã£ãŠãç察称ãªå¯Ÿè±¡ãèšè¿°ããããã®åºæºç³»ã¯(æ¹åæåã¯é¢ä¿ããŠããªããã)åç¹ã®åãæ¹ã®ã¿ãéèŠã§ãããäžæ¬¡å
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ã®å転ã«é¢ããå Žåã®ã¿ããç察称ã(spherical symmetry) ãšåŒã¶å Žåããããäžæ¬¡å
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ç©ç©ºéäžã§å®çŸ©ãããåœæ°ãå転äžå€ãããã¯ç察称(radial; ååŸç)ã§ãããšã¯ããã®å€ãåŒæ°ã«å¯Ÿããä»»æã®å転ã«é¢ããŠäžå€ãšãªãããšãèšããäŸãã°ãåœæ° f(x, y) = x + y ã¯åç¹åšãã®å¹³é¢å転ã®äžã§äžå€ã§ãããããäžè¬ã«ã空é X äžã®å€æãããã¯ãã®ãããªååã®æãåå空éäžã«äœçšããäœçšçŽ ã«å¯ŸããŠããX ã«ãããå転ãšäž¡ç«ããäœçšã«é¢ããæå³ã§ç察称æ§ã¯å®çŸ©ã§ãããäŸãã°äºæ¬¡å
ã®ã©ãã©ã¹äœçšçŽ Îf = âxxf + âyyf ã¯ãä»»æã®åè»¢å€æ r ã«å¯Ÿã㊠g(p) = f(r(p)) ãšãªãä»»æã®åå g ã«å¯Ÿã㊠(Îg)(p) = (Îf)(r(p)) ãæºãã(ã€ãŸãååã«å¯Ÿããå転ã¯åã«ãã®ã©ãã©ã·ã¢ã³ã«å¯Ÿããå転ã«ãªã)ãšããæå³ã«ãããŠç察称ã§ããã
ç©çåŠã«ãããå Žãç察称ã§ãããšããæŸå°ç¶å Ž (radial field) ãªã©ãšåŒã°ããããŸãç©ççãªç³»ããã®ç©ºéã«ãããåãã«äŸããåãå€ã瀺ããšãããã®ã©ã°ã©ã³ãžã¢ã³ã¯ç察称ã«ãªããããŒã¿ãŒã®å®çã«ããã°ãç©ççãªç³»ã®(ã©ã°ã©ã³ãžã¢ã³ã«å¯Ÿããæéã«é¢ããç©åã®)äœçšã¯å転äžå€ã§ãããåŸã£ãŠè§éåéã¯ä¿åãããã
| false | false | false |
https://ja.wikipedia.org/wiki/%E7%90%83%E5%AF%BE%E7%A7%B0
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7,713 |
極座æšç³»
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極座æšç³»(ããããã²ãããããè±: polar coordinates system)ãšã¯ãn 次å
ãŠãŒã¯ãªãã空é R äžã§å®çŸ©ããã1 åã®ååŸ r ãš n â 1 åã®åè§ Îž1, ..., Ξnâ1 ãããªã座æšã®ããšã§ãããç¹ S(0, 0, x3, ...,xn) ãé€ãçŽäº€åº§æšç³»ã¯ã屿çã«äžæçãªæ¥µåº§æšã«åº§æšå€æã§ããããS ã«ãããŠã¯ã€ã³ãã¢ã³ ã 0 ãšãªã£ãŠããŸããããäžæçãªæ¥µåº§æšè¡šçŸã¯äžå¯èœã§ãããããã¯ãS ã«æŒããåè§ãå®çŸ©ã§ããªãããšãããæããã§ããã
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ãŠãŒã¯ãªãã空é R ã«ãããæ¥µåº§æšã¯å座æš(circular coordinates)ãšåŒã°ããäžã€ã®ååŸåº§æšãšäžã€ã®è§åºŠåº§æšãããªããæãåçŽãªæ¥µåº§æšã§ãããrΞ å¹³é¢ã極座æšå¹³é¢(ãŸãã¯å¹³é¢æ¥µåº§æš)ãšããããç¹ç°ç¹ã¯ (r, Ξ) = (0, Ξ) å³ã¡ãxy座æšã§ã®åç¹ (x, y) = (0, 0) ã§ããã2 次å
å®ãã¯ãã«ç©ºéã«ãå®çŸ©ã§ããããšãããè€çŽ æ°äœ C äžã«ãå®çŸ©ã§ããããã®æãå座æšã極圢åŒãšåŒãã ããããããã®å Žåããªã€ã©ãŒã®å
¬åŒãå©çšã㊠z = re ãšè¡šããå座æšå¹³é¢äžã§åè§ãéå®ããªããã°ãããã¯xyå¹³é¢äžã§åãæãã
ååº§æš (r,Ξ) ããçŽäº€çŽç·åº§æš (x,y) ãžã®å€æã¯
{ x = r cos Ξ y = r sin Ξ {\displaystyle {\begin{cases}x=r\cos \theta \\y=r\sin \theta \\\end{cases}}}
ã§äžãããããè§åºŠåº§æšã®ç¯å²ã âÏ < Ξ â€ Ï ãšããå Žåã®çŽäº€çŽç·åº§æšããå座æšãžã®å€æã¯
{ r = x 2 + y 2 Ξ = sgn ( y ) arccos ( x / x 2 + y 2 ) {\displaystyle {\begin{cases}r={\sqrt {x^{2}+y^{2}}}\\\theta =\operatorname {sgn}(y)\arccos(x/{\sqrt {x^{2}+y^{2}}})\\\end{cases}}}
ã§äžãããããããã§ sgn ã¯ç¬Šå·é¢æ°ã§ãããåç¹ (x,y) = (0,0) ã«ãããŠç¹ç°æ§ãããã忝ããŒããšãªããã Ξ ãå®ãŸããªãã
å座æšã§ (0, 0) ãé€ã xy å¹³é¢äžã®å
šãŠã®ç¹ã衚çŸã§ãããããããã« z 軞ãå ããã°ãxyz 空éã衚çŸã§ããããããåç座æšç³»(cylindrical coordinates)ãšèšããåç座æšç©ºéäž(rΞz 空éäžãšããã)ã§ãΞ, z ãéå®ããªããã°ããã㯠xyz 空éäžã§åæ±ãæãããŸããåç座æšç©ºéäžã®ç¹ç°ç¹ã¯ z 軞äžã®å
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åçåº§æš (r,Ξ,z) ããçŽäº€çŽç·åº§æš (x,y,z) ãžã®å€æã¯
{ x = r cos Ξ y = r sin Ξ z = z {\displaystyle {\begin{cases}x=r\cos \theta \\y=r\sin \theta \\z=z\\\end{cases}}}
ã§äžããããçŽäº€çŽç·åº§æšããåç座æšãžã®å€æã¯
{ r = x 2 + y 2 Ξ = sgn ( y ) arccos ( x / x 2 + y 2 ) z = z {\displaystyle {\begin{cases}r={\sqrt {x^{2}+y^{2}}}\\\theta =\operatorname {sgn}(y)\arccos(x/{\sqrt {x^{2}+y^{2}}})\\z=z\\\end{cases}}}
ã§äžããããã
3 次å
ãŠãŒã¯ãªãã空é R ã«ãããæ¥µåº§æšç³»ãçé¢åº§æšç³»(Spherical coordinates)ãšãåŒã°ããã1 åã®ååŸ r ãš 2 åã®åè§ Îž, Ï ã«ãã£ãŠãªã(å³ãåç
§)ãçé¢åº§æšç³»ã«ãããŠãååŸãåºå®ãã2 åã®åè§ãåããã°ãxyz 空éäžã§çãæãã
ç座æšããçŽäº€çŽç·åº§æšãžã®å€æã¯
{ x = r sin Ξ cos Ï y = r sin Ξ sin Ï z = r cos Ξ {\displaystyle {\begin{cases}x=r\sin \theta \cos \phi \\y=r\sin \theta \sin \phi \\z=r\cos \theta \\\end{cases}}}
ã§äžããããçŽäº€çŽç·åº§æšããç座æšãžã®å€æã¯
{ r = x 2 + y 2 + z 2 Ξ = arccos ( z / x 2 + y 2 + z 2 ) Ï = sgn ( y ) arccos ( x / x 2 + y 2 ) {\displaystyle {\begin{cases}r={\sqrt {x^{2}+y^{2}+z^{2}}}\\\theta =\arccos(z/{\sqrt {x^{2}+y^{2}+z^{2}}})\\\phi =\operatorname {sgn}(y)\arccos(x/{\sqrt {x^{2}+y^{2}}})\\\end{cases}}}
ã§äžãããããz-è»žäž (x,y) = (0,0) ã«ãããŠç¹ç°æ§ãããã忝ããŒããšãªããã Ï ãå®ãŸããªããåç¹ã«ãããŠã¯ Ξ ãå®ãŸããªãã
極座æšå¹³é¢ã§ã®é·æ¹åœ¢ã¯ãçŽäº€åº§æšã«æŒããæåœ¢ã®äžéšãšãªããç¹ã« Ξ ã®é·ãã 2Ï ã§ããã°ãçŽäº€åº§æšã«ãããŠã¯åã®äžéšãšãªããr ã 0 ãã +â ãšããã°ããã®åã¯çŽäº€åº§æšå¹³é¢å
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šäœã¯ã極座æšå¹³é¢ã«æŒããé·æ¹åœ¢ãr à Ξ = [0, â) à [0, 2Ï) ã«çããã以äžã®ããšã¯åºçŸ©äºéç©åã«æŒããŠæçšã§ããããªããªãäžèšããã
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https://ja.wikipedia.org/wiki/%E6%A5%B5%E5%BA%A7%E6%A8%99%E7%B3%BB
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7,714 |
çŽäº€åº§æšç³»
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šãŠã®ç¹ã¯ãåã y 座æšã®å€ããšããšå®ããã
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| false | false | false |
https://ja.wikipedia.org/wiki/%E7%9B%B4%E4%BA%A4%E5%BA%A7%E6%A8%99%E7%B3%BB
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ãã㧠ε = t ( â A 0 A k ) 1 k {\displaystyle \epsilon =t(-{\frac {A_{0}}{A_{k}}})^{\frac {1}{k}}} ãšçœ®ããš f ( x c + t ( â A 0 A k ) 1 k ) = | A 0 ( 1 â t k ) + F ( t ) | {\displaystyle f(x_{c}+t(-{\frac {A_{0}}{A_{k}}})^{\frac {1}{k}})=|A_{0}(1-t^{k})+F(t)|}
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p = m R s T V {\displaystyle p={\frac {mR_{\text{s}}T}{V}}}
ã§è¡šããã質éå¯åºŠ m/V ãšæž©åºŠ T ã«æ¯äŸãããæ¯äŸä¿æ° Rs ã¯æ¯æ°äœå®æ°ãšåŒã°ãããä¿æ° Rs 㯠[ãšãã«ã®ãŒ]Ã[枩床]Ã[質é] ã®æ¬¡å
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žååŠã«åŸã N åã®èªç±ç²åãéã蟌ããããŠãããšããæž©åºŠ T ã®å¹³è¡¡ç¶æ
ã«ããããã®æ°äœã®å§å p ã¯
p = N k B T V {\displaystyle p={\frac {Nk_{\text{B}}T}{V}}}
ã§äžããããæ°å¯åºŠ N/V ãšæž©åºŠ T ã«æ¯äŸãããæ¯äŸä¿æ° kB ã¯æ°äœã®çš®é¡ã«ãããªãæ®é宿°ã§ããã«ããã³å®æ°ãšåŒã°ããã kB ã®æ¬¡å
㯠[ãšãã«ã®ãŒ]Ã[枩床] ã§ãããç²åæ° N ãåŒäžã«çŸããŠããããšããæãããªããã«ããã®ç¶æ
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ã«ããããçæ³æ°äœã®å§å p ã¯
p = n R T V {\displaystyle p={\frac {nRT}{V}}}
ã§è¡šãããã¢ã«äœç© V/n ã«åæ¯äŸããæž©åºŠ T ã«æ¯äŸãããæ¯äŸä¿æ° R ã¯æ°äœã®çš®é¡ã«ãããªãæ®é宿°ã§ãã¢ã«æ°äœå®æ°ãšåŒã°ãããR 㯠[ãšãã«ã®ãŒ]Ã[枩床]Ã[ç©è³ªé] ã®æ¬¡å
ãæã¡ããã®å€ã¯ãã«ããã³å®æ° kB ã«ã¢ãã¬ãã宿° NA ãæãããã®ã«çããããŸããæ¯æ°äœå®æ° RM ã«æ°äœã®ã¢ã«è³ªé M ãæãããã®ã«ãçããããã®ç¶æ
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U = 3 2 n R T = 3 2 N k B T {\displaystyle U={\frac {3}{2}}nRT={\frac {3}{2}}Nk_{\text{B}}T}
ã§è¡šãããããã®åŒããåååçæ³æ°äœã®å®ç©ã¢ã«ç±å®¹é CV, m ã¯
C V , m = 3 2 R {\displaystyle C_{V,{\text{m}}}={\frac {3}{2}}R}
ãšäžãããããåååçæ³æ°äœã® CV, m ã¯ã枩床ã«ãæ°äœã®çš®é¡ã«ãäŸããªã宿°ã§ããã
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U = c n R T = c N k B T {\displaystyle U=cnRT=cNk_{\text{B}}T}
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æ§æç²åãåäœãšã¿ãªããå Žåãæ¯äŸä¿æ° c ã¯ç²å1ååœããã®èªç±åºŠã® 1/2 ã«çžåœãããå
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žåççŽ CO 㯠c = 2.50 ã ããäºé
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žåç¡«é» SO2 㯠c = 3.80 ã§ãããäºååååã«éã£ãŠãå¡©çŽ Cl2 㯠c = 3.08 ã§ãã£ãŠã5/2 ãããããã 3 ã«è¿ããåžã¬ã¹ãé
žçŽ ãçªçŽ ãæ°Žèžæ°ãªã©ã®å°æ°ã®äŸå€ãé€ãã°ãæ¯äŸä¿æ° c ã¯åååŒããæèšç®ã§æ±ããããæ°å€ã§ã¯ãªãããã¡ã³ãã«ã¯ãŒã«ã¹å®æ° a, b ãšåæ§ã«ãæ¯äŸä¿æ° c ã¯å®éã®æ°äœã®ç±ååŠçæ§è³ªãåçŸããããã«å®ãããããã©ã¡ãŒã¿ã§ããããŸããåäœå転åãšã¯ã¿ãªããªãååã®æšæºå®ç©ç±å®¹éã¯ã枩床ã«ããå°ãªãããå€åãããããã«ãé¢ãããç矩ã®çæ³æ°äœãšããæ°äœã®çè«ã¢ãã«ããããŠèããã®ã¯ããšã³ããããŒãªã©ã®è¡šåŒãããããŠç°¡åã«ãªãããã§ããããŸããå
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žçŽ ãçªçŽ ãæ°Žèžæ°ã¯(çµé²ããªãéã)æ¯èŒçåºã枩床ã»å§åç¯å²ã§ç矩ã®çæ³æ°äœãšã¿ãªããã
枩床 Tã質é m ã®å¹³è¡¡ç¶æ
ã«ããããç矩ã®çæ³æ°äœã®å
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U = m c V T {\displaystyle U=mc_{V}T}
ã§è¡šããããç矩ã®çæ³æ°äœã®å®ç©æ¯ç±å®¹é cV ã¯ã枩床ã«äŸããªãæ°äœã«åºæã®å®æ°ã§ããã
ç±ååŠé¢æ°ãšããŠã¯ããšã³ããã㌠S ãäœç© Vãç©è³ªé n ãå
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U = U 0 + n â« T 0 T C V , m ( T â² ) d T â² = U 0 + m â« T 0 T c V ( T â² ) d T â² {\displaystyle U=U_{0}+n\int _{T_{0}}^{T}C_{V,{\text{m}}}(T')\,\mathrm {d} T'=U_{0}+m\int _{T_{0}}^{T}c_{V}(T')\,\mathrm {d} T'}
ã§è¡šããããããã§ U0 ã¯ã枩床 T0 ã«ãããç©è³ªé nã質é m ã®åçæ³æ°äœã®å
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C V , m ( T ) ⥠3 2 R {\displaystyle C_{V,{\text{m}}}(T)\geq {\frac {3}{2}}R}
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çæ³æ°äœã«æç«ããæ³åãšããŠä»£è¡šçãªãã®ã«ã¯æ¬¡ã®ãã®ããããããã
çæ³æ°äœã®çæž©å§çž®ç κT ã¯æ°äœã®çš®é¡ã«äŸããªãã
κ T = â 1 V ( â V ( T , p ) â p ) T = 1 p {\displaystyle \kappa _{T}=-{\frac {1}{V}}\left({\frac {\partial V(T,p)}{\partial p}}\right)_{T}={\frac {1}{p}}}
çæ³æ°äœã®ç±èšåŒµç α ã¯æ°äœã®çš®é¡ã«äŸããªãã
α = 1 V ( â V ( T , p ) â T ) p = 1 T {\displaystyle \alpha ={\frac {1}{V}}\left({\frac {\partial V(T,p)}{\partial T}}\right)_{p}={\frac {1}{T}}}
ã¢ãã¬ããã®æ³åã¯ãåäžå§åãåäžæž©åºŠã®æ¡ä»¶äžã§ã¯ãæ°äœã®çš®é¡ã«é¢ä¿ãªãåäœç©ã«åãæ°ã®ååãå«ããšãããã®ã ãã®æ³åã¯ãæ°äœã®æ§æç²åã®ååšãåæãšããªããã°æå³ãæããªãã
çæ³æ°äœã®æ··åæ°äœã«ã€ããŠããã®å§åãæ··åæ°äœãæ§æããåå¥ã®æ°äœã®åå§ã®åã§ãããšããæ³åã ãã®æ³åãæãç«ã€æ¡ä»¶ã¯ãæ°äœã®æ§æç²åã®ååšãåæãããåŠãã§ç°ãªãã
åçæ³æ°äœã®ãšã³ã¿ã«ã㌠H ã¯
H = U + p V = U + n R T {\displaystyle H=U+pV=U+nRT}
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H = U + n R T = n ( c + 1 ) R T {\displaystyle H=U+nRT=n(c+1)RT}
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T ãš n ãåãã§ããã°ãçæ³æ°äœã®ãšã³ã¿ã«ã㌠H 㯠V ã«ã p ã«ãäŸããã«åãå€ã«ãªã(ãžã¥ãŒã«ã®æ³å)ãçæ³æ°äœã¯çãšã³ã¿ã«ããŒèšåŒµã§æž©åºŠãå€åããªãã
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ç矩ã®çæ³æ°äœã®å®ç©ã¢ã«ç±å®¹é CV, m ã¯
C V , m = 1 n ( â U â T ) V = c R {\displaystyle C_{V,{\text{m}}}={\frac {1}{n}}\left({\frac {\partial U}{\partial T}}\right)_{V}=cR}
ã§è¡šãããå®å§ã¢ã«ç±å®¹é Cp, m ã¯
C p , m = 1 n ( â H â T ) p = ( c + 1 ) R {\displaystyle C_{p,{\text{m}}}={\frac {1}{n}}\left({\frac {\partial H}{\partial T}}\right)_{p}=(c+1)R}
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C p , m â C V , m = R {\displaystyle C_{p,{\text{m}}}-C_{V,{\text{m}}}=R}
ãšãªãããã®é¢ä¿ã¯ãã€ã€ãŒã®é¢ä¿åŒãšåŒã°ããããã®é¢ä¿åŒã¯åçæ³æ°äœã«ã€ããŠãæãç«ã€ããŸããçæ³æ°äœã®äºã€ã®ã¢ã«ç±å®¹éã®æ¯ γ ã¯æ¯ç±æ¯ãšåŒã°ã
γ = C p , m C V , m = C V , m + R C V , m = 1 + R C V , m {\displaystyle \gamma ={\frac {C_{p,{\text{m}}}}{C_{V,{\text{m}}}}}={\frac {C_{V,{\text{m}}}+R}{C_{V,{\text{m}}}}}=1+{\frac {R}{C_{V,{\text{m}}}}}}
ãšãªããåçæ³æ°äœã®æ¯ç±æ¯ γ ã¯äžè¬ã«ã¯æž©åºŠã«äŸåãããç矩ã®çæ³æ°äœã®å Žåã¯ãç±å®¹éãæž©åºŠã«äŸåããªãã®ã§
γ = 1 + 1 c {\displaystyle \gamma =1+{\frac {1}{c}}}
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ç矩ã®çæ³æ°äœã®ãšã³ããã㌠S ã¯
S = n R ln α T c V n {\displaystyle S=nR\ln \alpha {\frac {T^{c}V}{n}}}
ãšãªãããã㧠α ã¯ç©è³ªåºæã®å®æ°ã§ãããç矩ã®çæ³æ°äœã®ãšã³ããããŒã®åœ¢ã¯ãç±ååŠç¬¬äžæ³åãæºãããªãã
åçæ³æ°äœã®ãšã³ããã㌠S ã¯
S = n R ( ⫠T 0 T C V , m ( T Ⲡ) R T Ⲡd T Ⲡ+ ln α 0 V n ) {\displaystyle S=nR\left(\int _{T_{0}}^{T}{\frac {C_{V,{\text{m}}}(T')}{RT'}}\,\mathrm {d} T'+\ln \alpha _{0}{\frac {V}{n}}\right)}
ãšãªãããã㧠α0 ã¯ç©è³ªåºæã®å®æ°ã§ãããåçæ³æ°äœã® CV, m ã 3R/2 ãäžåãããšã¯ãªãã®ã§ãåçæ³æ°äœã®ãšã³ããããŒã®åœ¢ããŸããç±ååŠç¬¬äžæ³åãæºãããªãã
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T c V = const. {\displaystyle T^{c}V={\text{const.}}}
p V γ = const. {\displaystyle pV^{\gamma }={\text{const.}}}
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èªç¶ãªå€æ°ã§è¡šãã1æåçæ³æ°äœã®ãã«ã ãã«ãã®èªç±ãšãã«ã®ãŒ F(T, V, n) ããã³ã®ãã¹ã®èªç±ãšãã«ã®ãŒ G(T, p, n) ã¯ä»¥äžãšãªã:
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SOAP (ãããã³ã«)
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ã€ãªã³
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https://ja.wikipedia.org/wiki/%E3%83%AD%E3%83%BC%E3%83%9E%E5%B8%9D%E5%9B%BD
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7,802 |
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https://ja.wikipedia.org/wiki/%E3%82%AB%E3%82%A4%E3%83%AD_(%E6%9B%96%E6%98%A7%E3%81%95%E5%9B%9E%E9%81%BF)
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| false | false | false |
https://ja.wikipedia.org/wiki/%E7%94%9F%E5%8C%96%E5%AD%A6
|
7,850 |
1察1
|
1察1(one-to-one) ã®æå³:
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https://ja.wikipedia.org/wiki/1%E5%AF%BE1
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7,854 |
ç·åæ¹çšåŒç³»
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a 11 a 22 â a 12 a 21 â 0 {\displaystyle a_{11}a_{22}-a_{12}a_{21}\neq 0} ã®ãšã
ã§ããã a 11 a 22 â a 12 a 21 = 0 {\displaystyle a_{11}a_{22}-a_{12}a_{21}=0} ã®ãšãã | a 11 | 2 + | a 12 | 2 â 0 {\displaystyle |a_{11}|^{2}+|a_{12}|^{2}\neq 0} ã®ãšãã¯ãæ¹çšåŒã
ãšæžããŠã b 2 â k b 1 {\displaystyle b_{2}\neq kb_{1}} ã®ãšãè§£ãªãã b 2 = k b 1 {\displaystyle b_{2}=kb_{1}} ã®ãšã
ãšãªãã | a 11 | 2 + | a 12 | 2 = 0 {\displaystyle |a_{11}|^{2}+|a_{12}|^{2}=0} ã®ãšãã¯ãæ¹çšåŒã¯
ã§ããã | a 21 | 2 + | a 22 | 2 â 0 {\displaystyle |a_{21}|^{2}+|a_{22}|^{2}\neq 0} ã®ãšãã b 1 â 0 {\displaystyle b_{1}\neq 0} ã®ãšãè§£ãªãã b 1 = 0 {\displaystyle b_{1}=0} ã®ãšã
ãšãªãã | a 21 | 2 + | a 22 | 2 = 0 {\displaystyle |a_{21}|^{2}+|a_{22}|^{2}=0} ã®ãšãã | b 1 | 2 + | b 2 | 2 â 0 {\displaystyle |b_{1}|^{2}+|b_{2}|^{2}\neq 0} ã®ãšãè§£ãªãã b 1 = b 2 = 0 {\displaystyle b_{1}=b_{2}=0} ã®ãšã
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| false | false | false |
https://ja.wikipedia.org/wiki/%E7%B7%9A%E5%9E%8B%E6%96%B9%E7%A8%8B%E5%BC%8F%E7%B3%BB
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