Q: \uc548\ub155\ud558\uc138\uc694. \ubc14\ub85c \ubc11 \uc9c8\ubb38\uc744 \ud588\ub358 \ud559\uc0dd\uc778\ub370\uc694. \ubc11\uc5d0\ub2e4 \uc801\uc73c\uba74 \ubd88\ud3b8\ud558\uc2e4\uac83\uac19\uc544 \uc704\uc5d0\ub2e4 \uc801\uc5b4\ubd05\ub2c8\ub2e4. \uace1\uba74\uc744 \ub098\ud0c0\ub0bc\ub54c \uc9c1\uad50\uc88c\ud45c\uacc4\ub97c \uc4f0\uc9c0\uc54a\uc73c\uba74, \uadf8\ub7ec\ub2c8\uae4c \uac01\uc810\uc5d0 \uc811\ud558\ub294 \ubca1\ud130\uacf5\uac04\uc758 basis\ub4e4\uc774 \uc11c\ub85c \uc218\uc9c1\uc774 \uc544\ub2d0\uc218\ub3c4\uc788\uc73c\uba74 metric \uc744 \ud589\ub82c\ub85c \ud45c\ud604\ud560\ub54c \\(0\\) \uc774\uc544\ub2cc \ube44\ub300\uac01\uc131\ubd84\uc774 \ub098\ud0c0\ub09c\ub2e4\uace0 \uc54c\uace0\uc788\ub294\ub370\uc694. \ud568\uc218\uacf5\uac04\uc5d0\uc11c basis \ub97c \uc11c\ub85c \uc218\uc9c1\ud558\uc9c0\uc54a\uac8c \uc7a1\ub294\ub2e4\uba74 \ub0b4\uc801\uc744 \uc5b4\ub5bb\uac8c \ud45c\ud604\ud574\uc57c\ud558\ub098\uc694? \ubca1\ud130\uacf5\uac04\ub9cc \uc0dd\uac01\ud574\ubcf4\uc544\ub3c4 \uc800\uc5d0\uac8c\ub294 \ub108\ubb34 \uc5b4\ub835\ub124\uc694. \uc9c0\ub09c\ubc88 \uac00\ub974\uccd0\uc8fc\uc2e0\ub300\ub85c \ub0b4\uc801 $ xu+yv $ \ub97c $ g_{11}xu+g_{22}yv (g_{12}=g_{21}=0) $ \uc73c\ub85c \ubc14\uafb8\ub294\uac83\uc774 <\/p>\n
\\[ \\langle f,g\\rangle = \\int_{-\\infty}^{+\\infty}f^{*}(x)h(x)g(x)dx \\] <\/p>\n
\uc5d0 \ud574\ub2f9\ud558\ub294 \uac83\ucc98\ub7fc \\[ \\langle (x,y),(u,v) \\rangle = g_{11} xu + g_{12} xv + g_{21} yu + g_{22} yv \\] \uc740 \ud568\uc218\uacf5\uac04\uc758 \uc5b4\ub5a4 \ub0b4\uc801\uc5d0 \ud574\ub2f9\ud558\ub294\uc9c0 \uad81\uae08\ud569\ub2c8\ub2e4. \uc544 \uadf8\ub9ac\uace0 \uc9c0\ub09c\ubc88 \ub2f5\ubcc0 \uac10\uc0ac\ub4dc\ub9bd\ub2c8\ub2e4.- \uc720\uc0c1\ud604 <\/p>\n
A: \ub098\ub3c4 \ubcc4\ub85c \uc0dd\uac01\ud574 \ubcf4\uc9c0 \uc54a\uc544\uc11c \uadf8\ub0e5\uc740 \uc798 \ubaa8\ub974\uaca0\ub124\uc694. \uc544, \ubcf4\ud1b5 Hilbert \uacf5\uac04\uc5d0\uc11c\ub294 \uc9c1\uad50\uc88c\ud45c\ub97c \uc798 \uc4f0\uace0\uc694, \uc9c1\uad50\uc88c\ud45c\uc5d0\uc11c\ub294 \uc131\ubd84\uc758 \uacf1\uc758 (\ubb34\ud55c)\ud569\uc73c\ub85c \ub0b4\uc801\uc744 \ub098\ud0c0\ub0bc \uc218 \uc788\uc73c\ub2c8\uae4c \uc774\uac83\uc758 \uc911\uac04\uc5d0 (\ubb34\ud55c)\ud589\ub82c\uc744 \ub123\uc5b4\uc11c $ {}^tXAY $ \ucc98\ub7fc \uc4f0\ub294 \uac83\uc774\uba74 \ub418\uaca0\uc9c0\uc694. \uc77c\ubc18\uc801\uc73c\ub85c\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \ub098\ud0c0\ub0b4\uc57c \ud558\uaca0\ub124\uc694: $ A $ \ub294 positie definite\uc778 linear transformation\uc73c\ub85c \ud568\uc218\uacf5\uac04\uc5d0\uc11c \uc790\uae30 \uc790\uc2e0\uc73c\ub85c \uc815\uc758\ub41c \uac83\uc73c\ub85c \ud558\uba74 \uc0c8 \ub0b4\uc801\uc740 <\/p>\n
$ ⟨ X,AY ⟩ $ <\/p>\n
\uc774\ub77c\uace0 \uc4f0\uba74 \ub418\uaca0\ub124\uc694. \uc5ec\uae30\uc11c \uad04\ud638\ub294 \uba3c\uc800 \uc4f0\ub358 \ub0b4\uc801\uc784. \uc774\ub7f0 A\uc758 \uc608\ub294 \ud568\uc218\ub97c \uc9c1\uad50basis\uc5d0 \ub300\ud558\uc5ec \uc37c\uc744 \ub54c\ub294 \uc704\uc640 \uac19\uc774 \ud589\ub82c\uaf34\ub85c \uc368 \ubcfc \uc218 \uc788\uc744 \uac83 \uac19\uace0\uc694, \uadf8\ub807\uc9c0 \uc54a\uace0 \uc9c1\uc811 \ud568\uc218\uc5d0 \uc791\uc6a9\ud558\ub294 \uc608\ub85c \uc798 \uc54c\ub824\uc9c4 \uac83\uc740 <\/p>\n
$ I + Δ $ <\/p>\n
\uac19\uc740 \uac83\uc744 \ub4e4 \uc218 \uc788\uc5b4\uc694. \uc5ec\uae30\uc11c I \ub294 \ub2e8\uc704\uc0ac\uc0c1 $ v → v$ \uc774\uace0 $ Δ $ \ub294 Laplacian \uc989, $ x $ \uc5d0 \ub300\ud558\uc5ec \ub450 \ubc88 \ubbf8\ubd84\ud558\uace0 \uadf8 \uacb0\uacfc\uc5d0 \ub9c8\uc774\ub108\uc2a4 \ubd80\ud638\ub97c \ubd99\uc5ec\uc8fc\ub294 \uc0ac\uc0c1\uc785\ub2c8\ub2e4. – \uae40\uc601\uc6b1 <\/p>\n
-— Q: \ubbf8\ubd84\uae30\ud558\ud559\uc744 \ubc30\uc6b0\ub358 \ub3c4\uc911 \ub5a0\uc624\ub978 \uc9c8\ubb38\uc774 \uc788\uc5b4\uc11c \uc774\ub807\uac8c \uc9c8\ubb38\ud558\uac8c\ub418\uc5c8\uc2b5\ub2c8\ub2e4. \ub0b4\uc801 <\/p>\n
\\[ ds^2 = E(u,v)du^2 + 2F(u,v)dudv + G(u,v)dv^2 \\] <\/p>\n
\uc5d0\uc11c \uace1\uba74\uc758 \uac01\uc810 (u,v) \ub9c8\ub2e4 E,F,G\uc758 \uac12\uc774 \ub2ec\ub77c\uc9c0\uace0 \ub0b4\uc801\uc774 \ub2ec\ub77c\uc9c0\uba74\uc11c \ud718\uc5b4\uc9c4\uace1\uba74\uc744 \ub098\ud0c0\ub0b4\uac8c \ub41c\ub2e4\uace0 \ubc30\uc6e0\ub294\ub370\uc694. \ud3c9\uba74\uc740 \ud718\uc5b4\uc9c0\uc9c0\uc54a\uace0 E,F,G\uc758 \uac12\uc774 \uc77c\uc815\ud55c \ubca1\ud130\uacf5\uac04\uc774\ub77c\ub294\uac83\ub3c4 \ubc30\uc6e0\uc2b5\ub2c8\ub2e4. \uadf8\ub7f0\ub370 \ud568\uc218\ub4e4\uc774 \ubaa8\uc5ec\uc788\ub294 \uacf5\uac04\ub3c4 \ubca1\ud130\uacf5\uac04\uc774\ub77c\ub294\uac83\uc744 \ubc30\uc6e0\uac70\ub4e0\uc694. \uadf8\ub9ac\uace0 \ubcf4\ud1b5 \ud568\uc218\uacf5\uac04\uc5d0\uc11c \ub0b4\uc801\uc774 <\/p>\n
\\[ \\langle f,g\\rangle = \\int_{-\\infty}^{+\\infty}f^{*}(x)g(x)dx \\] <\/p>\n
\uc774\ub807\uac8c \uc8fc\uc5b4\uc9c0\ub294 \uacbd\uc6b0\uac00 \ub9ce\ub354\ub77c\uad6c\uc694.( $ f(x) $ \uc758 \ucf24\ub808\ubcf5\uc18c\uc218\ub97c $ f^{*}(x) $ \ub77c\uace0 \uc37c\uc2b5\ub2c8\ub2e4.) \ud568\uc218\uacf5\uac04\ub3c4 \ubca1\ud130\uacf5\uac04\uc774\ub77c \ud3c9\uba74\uacfc \ube44\uc2b7\ud55c \uc77c\uc885\uc758 \ud3c9\ud3c9\ud55c \uacf5\uac04\uc774\ub77c\uace0 \ubcfc\uc218\ub3c4 \uc788\uc744\uac83\uac19\uc740\ub370\uc694. ds^2 \uc758 E,F,G\uac12\uc774 \uace1\uba74\uc758 \uac01\uc810\ub9c8\ub2e4 \ub2ec\ub77c\uc9c0\uba74\uc11c \ud718\uc5b4\uc9c4\uace1\uba74\uc744 \ub098\ud0c0\ub0b4\ub294\uac83\ucc98\ub7fc $ ⟨ f,g⟩ = ∫_{-∞}^{+∞}f^{*}(x) [ XXX ]g(x)dx $ \uc758 $ [XXX] $ \uc548\uc5d0 (E,F,G\uc640 \ube44\uc2b7\ud558\uac8c) \ud568\uc218\uacf5\uac04\uc758 \uac01\uc810\ub9c8\ub2e4 \uac12\uc774 \ubc14\ub00c\ub294 \ubb34\uc5b8\uac00\uac00 \ub4e4\uc5b4\uac00\uba74 \ud718\uc5b4\uc9c4\ud568\uc218\uacf5\uac04(?)\uac19\uc740\uac78 \ub098\ud0c0\ub0b4\uac8c\ub418\ub294\uac8c \uc544\ub2d0\uae4c \ud558\ub294 \uc0dd\uac01\uc774 \ub4e4\uc5c8\uc2b5\ub2c8\ub2e4. \uadf8\ub7f0\uac83\uc774 \uc788\uc744\uc218\uc788\ub294\uc9c0 \uc54c\uace0\uc2f6\uc5b4\uc11c \uc9c8\ubb38\ud558\uac8c\ub418\uc5c8\uc2b5\ub2c8\ub2e4. \uc9e7\uac8c \uc4f0\ub824\uace0\ud588\ub294\ub370 \ub108\ubb34 \uae38\uc5b4\uc84c\ub124\uc694. \uc8c4\uc1a1\ud569\ub2c8\ub2e4. \uadf8\ub7fc \ub2f5\ubcc0\uae30\ub2e4\ub9ac\uaca0\uc2b5\ub2c8\ub2e4. \uac10\uc0ac\ud569\ub2c8\ub2e4. – \ubb3c\ub9ac\ud559\uacfc \uc720\uc0c1\ud604 <\/p>\n
A: \uc88b\uc740 \uc9c8\ubb38\uc785\ub2c8\ub2e4. \uc704\uc758 \uc0dd\uac01\uc5d0\uc11c \uc911\uc694\ud55c \uac83\uc740 \ud568\uc218\ub4e4\uc758 \uacf5\uac04\uc5d0\uc11c \uc810(\ubca1\ud130)\ub294 \ud568\uc218 $ f,g $ \ub77c\ub294 \uac83\uc744 \uc78a\uc9c0 \ub9d0\uae30 \ubc14\ub798\uc694. \uadf8\ub7ec\ub2c8\uae4c \uac01 \uc810\uc5d0\uc11c \ub0b4\uc801\uc774 \ubc14\ub010\ub2e4\ub294 \uac83\uc740 $ f $ \uc640 \uac19\uc740 \uc810\uc774 \ubc14\ub00c\uba74 \ub0b4\uc801\uc774 \ubc14\ub010\ub2e4\ub294 \uac83\uc774\uc9c0\uc694. \uc870\uae08 \ubcf5\uc7a1\ud558\uc9c0\ub9cc \ud558\ub098 \ud558\ub098 \ub530\uc838\uc11c \uc120\ud615\ub300\uc218\uc640 \uc0c8\ub85c\uc6b4 \uacf5\uac04\uc744 \ube44\uad50\ud574\ubcf4\uba74 \ub429\ub2c8\ub2e4. <\/p>\n
\uc6b0\uc120 \uc704\uc5d0\uc11c \ub9d0\ud558\ub294 \uac1c\ub150\uc740 \ubca1\ud130\uacf5\uac04\uc744 \ubb34\ud55c\ucc28\uc6d0\uc73c\ub85c \ubc14\uafbc \ud568\uc218\uacf5\uac04\uc774\uace0 \uc774\uc5d0 \ub300\ud55c \uc774\ub860\uc740 \ubcf4\ud1b5 \ud568\uc218\ud574\uc11d\ud559\uc774\ub77c\ub294 \uacfc\ubaa9\uc5d0\uc11c \uacf5\ubd80\ud569\ub2c8\ub2e4. \ubb34\ud55c\ucc28\uc6d0\ubca1\ud130\uacf5\uac04\ub860\uc774\uc8e0. \uc5ec\uae30\uc5d0 \ub0b4\uc801\uc774 \uc8fc\uc5b4\uc9c4 \uacbd\uc6b0\ub294 Hilbert\uacf5\uac04\ub860\uc774\ub77c\uace0 \ud558\uace0\uc694. \uadf8\ub7f0\ub370 \uac01 \uc810\ub9c8\ub2e4 \uc811\ud3c9\uba74\uc774 \uc774\ub7f0 Hilbert\uacf5\uac04\uc774 \ub418\uc5b4\uc11c \uc704\uc640 \uac19\uc740 \ub0b4\uc801\uc744 \uc0ac\uc6a9\ud558\uc5ec\uc57c \ub418\ub294 \uacf5\uac04\uc740 Hilbert \ub2e4\uc591\uccb4(manifild)\ub77c \ud558\ub294\ub370 \uc774\ub7f0 \uacf5\uac04\uc744 \uc0dd\uac01\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uc774\ub7f0 \ub0b4\uc6a9\uc744 \uacf5\ubd80\ud558\ub294 \uac83\uc740 \uc774\ub984\uc774 Global Analysis(\ub300\uc5ed\ud574\uc11d\ud559)\uc774\ub77c\uace0 \ud558\ub294 \ubd84\uc57c\uc5d0\uc11c \ub2f4\ub2f9\ud558\ub294\ub370 \uadf8 \uc774\uc720\ub294 \uc774\ub7f0 \uacf5\uac04\uc758 \uc774\ub860\uc5d0\uc11c \uac00\uc7a5 \uc5b4\ub824\uc6b4 \uac83\uc774 \ud3b8\ubbf8\ubd84\ubc29\uc815\uc2dd\uc774\uae30 \ub54c\ubb38\uc785\ub2c8\ub2e4. \uc774 \ubd80\ubd84\uc740 1970\ub144 \uc804\ud6c4\ud574\uc11c \ub9ce\uc774 \uc5f0\uad6c\ub418\uc5c8\ub294\ub370 \uc694\uc988\uc74c\uc740 \uc870\uae08 \ub738\ud55c \ud3b8\uc785\ub2c8\ub2e4. \uae30\ucd08\uc801\uc778 \uc815\uc758\ub294 Serge Lang\uc758 (Introduction to) differentiable manifolds \ub77c\ub294 \ucc45\uc5d0 \uc798 \ub098\uc640 \uc788\uace0 \uc774 \ucc45\uc740 \ub0b4\uc801\ubcf4\ub2e4\ub294 Norm(\ubca1\ud130\uc758 \ud06c\uae30)\ub9cc \uc8fc\uc5b4\uc9c4 Banach manifold(\ubc14\ub098\ud06c \ub2e4\uc591\uccb4)\uc5d0 \ub300\ud558\uc5ec \uc4f0\uc5ec \uc788\uc5b4\uc694. \uc27d\uac8c \uc77d\uc744 \uc218 \uc788\ub294 \ub2e4\ub978 \ucc45\uc740 \uc5bc\ub978 \uc0dd\uac01\ub098\uc9c0 \uc54a\ub124\uc694. <\/p>\n
\uc774\uc81c \uc704\uc5d0\uc11c \ubb3c\uc5b4\ubcf8 \uac83\uc744 \uc870\uae08 \uc0b4\ud3b4\ubcf4\uba74 \ud568\uc218\uacf5\uac04\uc758 \ub0b4\uc801 <\/p>\n
\\[ \\langle f,g\\rangle = \\int_{-\\infty}^{+\\infty}f^{*}(x)g(x)dx \\] <\/p>\n
\uc744 <\/p>\n
\\[ \\langle f,g\\rangle = \\int_{-\\infty}^{+\\infty}f^{*}(x)h(x)g(x)dx \\] <\/p>\n
\uc640 \uac19\uc774 \ubc14\uafb8\ub294 \uac83\uc740 \ub9c8\uce58 \ub0b4\uc801 $ xu+yv $ \ub97c $ axu+byv $ \uc640 \uac19\uc774 \ubc14\uafb8\ub294 \uac83\uc774\uace0 \uc774\uac83\uc740 \ub2e8\uc21c\ud788 \ubca1\ud130\uacf5\uac04\uc5d0\uc11c\uc758 \ub0b4\uc801\uc744 \ubc14\uafb8\ub294 \uac83\uc5d0 \ud574\ub2f9\ud569\ub2c8\ub2e4. \ub530\ub77c\uc11c \uc6d0\ud558\ub294 \uc2dd\uc73c\ub85c \uad6c\ubd80\ub7ec\uc9c4 \uacf5\uac04\uc744 \uc0dd\uac01\ud558\ub294 \uac83\uc740 \uac01 \uc810\uc774 \ud568\uc218\uac19\uc740 \uac83\ub4e4\uc774\uace0 \uc774\uac83\uc758 \uc811\ud3c9\uba74\ubc29\ud5a5\ub3c4 \ud568\uc218\ub4e4\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uac83\uc744 \uc0dd\uac01\ud574\uc57c \ud558\uc9c0\uc694. <\/p>\n
\uc608\ub97c \ub4e4\uba74, \ud568\uc218\ub4e4\ub85c\uc11c $ ∫_0^1 |f(x)|^2 dx =1 $ \uc744 \ub9cc\uc871\ud558\ub294 $ f $ \ub4e4\uc758 \uc9d1\ud569\uc744 \uc0dd\uac01\ud558\uba74 \ub3fc\uc694. \uc774\uac83\uc740 \ub9c8\uce58 \ubcf4\ud1b5 \ubca1\ud130\uacf5\uac04\uc5d0\uc11c \uad6c\uba74(\uc6d0)\uc744 \uc0dd\uac01\ud558\ub294 \uac83\uacfc \uac19\uc544\uc694. \uc774 \uba74\uc758 \uac01\uc810\uc5d0\uc11c \uc811\uc120\ubc29\ud5a5\uc744 \ubaa8\ub450 \uc0dd\uac01\ud558\uba74 \ubb34\ud55c\ucc28\uc6d0 \ubca1\ud130\uacf5\uac04\uc774 \ub418\uba70 \uadf8 \uc6d0\uc18c\ub294 \ub2e4\uc2dc \ud568\uc218\uac00 \ub418\ub294\ub370 \uc774 \ub0b4\uc801\uc740 \uc810\uc5d0 \ub530\ub77c\uc11c \ub2e4\ub978 \uacf5\uac04\uc758 \ub0b4\uc801\uc774 \ub429\ub2c8\ub2e4. \uc989 \uc810\uc5d0 \ub530\ub77c \ubca1\ud130\uacf5\uac04 \uc790\uccb4\uac00 \ubc14\ub01d\ub2c8\ub2e4. \uc870\uae08 \ub354 \ubcf5\uc7a1\ud55c \uacf5\uac04\uc740 $ ∫_0^1 h(x)|f(x)|^2dx=1 $ \uc73c\ub85c \uc815\uc758\ub41c $ f $ \ub4e4\uc758 \uace1\uba74\uc744 \uc0dd\uac01\ud558\uba74 \ub429\ub2c8\ub2e4. <\/p>\n
Q : \uc790\uc138\ud558\uac8c \ub2f5\ubcc0\ud574\uc8fc\uc154\uc11c \uc815\ub9d0 \uc815\ub9d0 \uc9c4\uc2ec\uc73c\ub85c \uac10\uc0ac\ub4dc\ub9bd\ub2c8\ub2e4. \ub610 \uc5ec\ucb48\uc5b4\ubcfc\uac83\uc774 \uc788\ub294\ub370\uc694… \uc608\ub85c \ub4e4\uc5b4\uc8fc\uc2e0 \\(\\int^{1}_0 |f(x)|^2 dx = 1\\) \uc744 \ub9cc\uc871\ud558\ub294 $ f $ \ub4e4\uc758 \uc9d1\ud569\uc5d0\uc11c \uac01 \uc810\uc5d0 \uc811\ud558\ub294 \ubca1\ud130\uacf5\uac04\uc744 \uacc4\uc0b0\ud574\ubcf4\uace0\uc2f6\uc740\ub370\uc694. \uc791\ub144 \ubbf8\ubd84\uae30\ud558\ud559\uc5d0\uc11c \ucc98\uc74c \ubc30\uc6e0\uc744\ub54c\ub294 2\ucc28\uc6d0\uace1\uba74\uc744 3\ucc28\uc6d0 \uc720\ud074\ub9ac\ub4dc\uacf5\uac04 \uc548\uc5d0 \ub4e4\uc5b4\uc788\ub2e4\uace0 \uc0dd\uac01\ud55c \ub4a4 \uace1\uba74\uc744 \ub098\ud0c0\ub0b4\ub294 \ubc29\ubc95\uc744 \uacf5\ubd80\ud588\uc5c8\ub294\ub370\uc694. \uc774 \ubc29\ubc95\uacfc \ube44\uc2b7\ud55c \ubc29\ubc95\uc744 \uc4f0\uba74 \ub420\uac83\uac19\uae30\ub294 \ud55c\ub370 \uad6c\uccb4\uc801\uc778 \uacc4\uc0b0\ubc29\ubc95\uc744 \ubaa8\ub974\uaca0\ub124\uc694. \ub354 \ub192\uc740 \uc218\uc900\uc758 \uc774\ub860\uc744 \ubc30\uc6cc\uc57c \uacc4\uc0b0\uc774 \uac00\ub2a5\ud55c\uac00\uc694? \uadf8\ub9ac\uace0 \ud558\ub098 \ub354 \uad81\uae08\ud55c\uac83\uc774 \uc788\ub294\ub370\uc694. 2\ucc28\uc6d0\uace1\uba74\uc774 3\ucc28\uc6d0\uc720\ud074\ub9ac\ub4dc\uacf5\uac04\uc548\uc5d0 \ub4e4\uc5b4\uc788\ub2e4\uace0 \uac00\uc815\ud558\uc9c0\uc54a\uace0, \ub9ac\ub9cc\uae30\ud558\ud559\uc5d0\uc11c\ub294 \ucc98\uc74c\ubd80\ud130 2\ucc28\uc6d0\uace1\uba74\uc744 \ub3c5\ub9bd\uc801\uc778 \uacf5\uac04\uc774\ub77c \uc0dd\uac01\ud55c\ub4a4 3\ucc28\uc6d0\uc720\ud074\ub9ac\ub4dc\uacf5\uac04\uc5d0 \ub300\ud55c \uc5b8\uae09\uc774 \uc804\ud600\uc5c6\uc774\ub3c4 \uace1\uba74\uc744 \ub098\ud0c0\ub0b8\ub2e4\ub294 \uac83\uc744 \ubc30\uc6e0\ub294\ub370\uc694, \uc774\uac83\uacfc \ube44\uc2b7\ud55c \ubc29\ubc95\uc744 \uc368\uc11c\ub3c4 \uc811\uacf5\uac04\uc774 \ud568\uc218\uacf5\uac04\uc774 \ub418\ub294 \uacf5\uac04\uc744 \ub098\ud0c0\ub0bc\uc218 \uc788\uc744\uae4c\uc694? – \uc720\uc0c1\ud604 (Date(2007-01-23T19:14:27)) <\/p>\n
A: \uc6b0\uc120 \uc774 \uace1\uba74\uc740 \uad6c\uba74\uc774\uae30 \ub54c\ubb38\uc5d0 \uc774 \uace1\uba74 \uc704\uc758 \ud55c \uc810 $ f $ \uc5d0\uc11c\uc758 \uc811\ud3c9\uba74\uc740 $ f $ \uc640 \uc218\uc9c1\uc778 $ g $ \uc804\uccb4\uc758 \uc9d1\ud569\uc774\ub77c\uace0 \ud558\uba74 \ub429\ub2c8\ub2e4.(\uc26c\uc6b4 \uacbd\uc6b0\uc8e0.) \uadf8\ub7ec\ub2c8\uae4c $ ∫_0^1 f^*(x) g(x) dx=0 $ \uc778 $ g $ \ub97c \uc0dd\uac01\ud558\uba74 \ub418\uc8e0. \uc774\ub7f0 $ g $ \ub4e4\uc5d0 \ub300\ud574\uc11c \ub0b4\uc801\uc744 \uc704\uc640 \uac19\uc774 \uc368\uc11c \uacc4\uc0b0\ud569\ub2c8\ub2e4. \ub458\uc9f8 \uc9c8\ubb38\uc740 \uc6b0\uc120 \uacf5\uac04\uc744 \uc7a1\uace0 \uacf5\uac04\uc758 \uac01 \uc810 $ f $ \ub9c8\ub2e4 \uadf8 \uacf5\uac04\uacfc \ub611 \uac19\uc740 \uacf5\uac04\uc744 \uc811\uacf5\uac04\uc774\ub77c\uace0 \uc0dd\uac01\ud569\ub2c8\ub2e4. \uc774 \uacf5\uac04\uc744 $ X $ , \uc811\uacf5\uac04\uc744 $ T_fX $ \ub77c\uace0 \ud558\uae30\ub85c \ud558\uc8e0. \uadf8\ub9ac\uace0 $ T_fX $ \ub294 $ X $ \uc640 \ub611 \uac19\uc740 \ubaa8\uc591\uc758 \uacf5\uac04\uc785\ub2c8\ub2e4. \uc774\uc81c $ T_fX $ \uc5d0 \ub0b4\uc801\uc744 \uc815\uc758\ud558\ub294\ub370 \uc704\uc5d0\uc11c\uc640 \uac19\uc774 $ h(x) $ \ub97c \uc368\uc11c \uc815\uc758\ud558\ub294 \uac83\uc778\ub370 \uc774 $ h(x) $ \uac00 \ub9e4 $ f $ \ub9c8\ub2e4 \ub2ec\ub77c\uc9c0\ub3c4\ub85d \ud558\uba74 \ub429\ub2c8\ub2e4. \uc989, <\/p>\n
$ ⟨ g_1,g_2 ⟩ = ∫_0^1 g_1^*(x)g_2(x) h_f(x) dx $ <\/p>\n
\ub77c\uace0 \uc7a1\uc544\ubcf4\uba74 \uc810 $ f $ \uac00 \ubcc0\ud558\ub294\ub370 \ub530\ub77c\uc11c \ub0b4\uc801\uc774 \ubcc0\ud558\ub294 \uac83\uc774 \ub418\uc9c0\uc694. – [\uae40\uc601\uc6b1] (DateTime(2007-01-24T02:51:07)) <\/p>\n","protected":false},"excerpt":{"rendered":"
Q: \uc548\ub155\ud558\uc138\uc694. \ubc14\ub85c \ubc11 \uc9c8\ubb38\uc744 \ud588\ub358 \ud559\uc0dd\uc778\ub370\uc694. \ubc11\uc5d0\ub2e4 \uc801\uc73c\uba74 \ubd88\ud3b8\ud558\uc2e4\uac83\uac19\uc544 \uc704\uc5d0\ub2e4 \uc801\uc5b4\ubd05\ub2c8\ub2e4. \uace1\uba74\uc744 \ub098\ud0c0\ub0bc\ub54c \uc9c1\uad50\uc88c\ud45c\uacc4\ub97c \uc4f0\uc9c0\uc54a\uc73c\uba74, \uadf8\ub7ec\ub2c8\uae4c \uac01\uc810\uc5d0 \uc811\ud558\ub294 \ubca1\ud130\uacf5\uac04\uc758 basis\ub4e4\uc774 \uc11c\ub85c \uc218\uc9c1\uc774 \uc544\ub2d0\uc218\ub3c4\uc788\uc73c\uba74 metric \uc744 \ud589\ub82c\ub85c \ud45c\ud604\ud560\ub54c \\(0\\) \uc774\uc544\ub2cc \ube44\ub300\uac01\uc131\ubd84\uc774 \ub098\ud0c0\ub09c\ub2e4\uace0 \uc54c\uace0\uc788\ub294\ub370\uc694. \ud568\uc218\uacf5\uac04\uc5d0\uc11c basis \ub97c \uc11c\ub85c \uc218\uc9c1\ud558\uc9c0\uc54a\uac8c \uc7a1\ub294\ub2e4\uba74 \ub0b4\uc801\uc744 \uc5b4\ub5bb\uac8c \ud45c\ud604\ud574\uc57c\ud558\ub098\uc694? \ubca1\ud130\uacf5\uac04\ub9cc \uc0dd\uac01\ud574\ubcf4\uc544\ub3c4 \uc800\uc5d0\uac8c\ub294 \ub108\ubb34 \uc5b4\ub835\ub124\uc694. \uc9c0\ub09c\ubc88 \uac00\ub974\uccd0\uc8fc\uc2e0\ub300\ub85c \ub0b4\uc801 $ xu+yv $ \ub97c $ … \ub354 \uc77d\uae30<\/a><\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-3744","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"distributor_meta":false,"distributor_terms":false,"distributor_media":false,"distributor_original_site_name":"\uae40\uc601\uc6b1","distributor_original_site_url":"https:\/\/mathematicians.korea.ac.kr\/ywkim","push-errors":false,"_links":{"self":[{"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts\/3744","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/comments?post=3744"}],"version-history":[{"count":1,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts\/3744\/revisions"}],"predecessor-version":[{"id":3745,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts\/3744\/revisions\/3745"}],"wp:attachment":[{"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/media?parent=3744"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/categories?post=3744"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/tags?post=3744"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}