[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/10857#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/10857","headline":"\u533a\u5206\u884c\u5217 – Wikipedia","name":"\u533a\u5206\u884c\u5217 – Wikipedia","description":"\u533a\u5206\u884c\u5217\uff08\u304f\u3076\u3093\u304e\u3087\u3046\u308c\u3064\uff09\u3082\u3057\u304f\u306f\u30d6\u30ed\u30c3\u30af\u884c\u5217 (block matrix) \u3068\u306f\u3001\u3044\u304f\u3064\u304b\u306e\u9577\u65b9\u5f62\u306e\u30d6\u30ed\u30c3\u30af\u306b\u300c\u533a\u5206\u3051\u300d\u3055\u308c\u305f\u884c\u5217\u3067\u3042\u308b\u3002 \u4f8b\u3048\u3070\u30014\u3064\u306e\u884c\u5217 A=[2\u221215\u221214181\u22122],B=[\u2212361341],C=[\u2212426],D=[91]{displaystyle A={begin{bmatrix}2&-1&5-1&4&18&1&-2end{bmatrix}},quad B={begin{bmatrix}-3&61&34&1end{bmatrix}},quad C={begin{bmatrix}-4&2&6end{bmatrix}},quad D={begin{bmatrix}9&1end{bmatrix}}} \u3092\u4e26\u3079\u3066\u3067\u304d\u308b 4 \u00d7 5 \u884c\u5217 [ABCD]=[2\u221215\u221236\u22121411381\u2212241\u221242691]{displaystyle {begin{bmatrix}A&BC&Dend{bmatrix}}={begin{bmatrix}2&-1&5&&-3&6-1&4&1&&1&38&1&-2&&4&1&&&&&-4&2&6&&9&1end{bmatrix}}} \u3092\u3001A, B, C,","datePublished":"2018-01-30","dateModified":"2022-09-14","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/cd810e53c1408c38cc766bc14e7ce26a?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/cd810e53c1408c38cc766bc14e7ce26a?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/eece18e5b2b88432f9ed933076e541e3f07cc5cc","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/eece18e5b2b88432f9ed933076e541e3f07cc5cc","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/10857","about":["Wikipedia"],"wordCount":4914,"articleBody":"\u533a\u5206\u884c\u5217\uff08\u304f\u3076\u3093\u304e\u3087\u3046\u308c\u3064\uff09\u3082\u3057\u304f\u306f\u30d6\u30ed\u30c3\u30af\u884c\u5217 (block matrix) \u3068\u306f\u3001\u3044\u304f\u3064\u304b\u306e\u9577\u65b9\u5f62\u306e\u30d6\u30ed\u30c3\u30af\u306b\u300c\u533a\u5206\u3051\u300d\u3055\u308c\u305f\u884c\u5217\u3067\u3042\u308b\u3002  \u4f8b\u3048\u3070\u30014\u3064\u306e\u884c\u5217A=[2\u221215\u221214181\u22122],B=[\u2212361341],C=[\u2212426],D=[91]{displaystyle A={begin{bmatrix}2&-1&5-1&4&18&1&-2end{bmatrix}},quad B={begin{bmatrix}-3&61&34&1end{bmatrix}},quad C={begin{bmatrix}-4&2&6end{bmatrix}},quad D={begin{bmatrix}9&1end{bmatrix}}}\u3092\u4e26\u3079\u3066\u3067\u304d\u308b 4 \u00d7 5 \u884c\u5217  [ABCD]=[2\u221215\u221236\u22121411381\u2212241\u221242691]{displaystyle {begin{bmatrix}A&BC&Dend{bmatrix}}={begin{bmatrix}2&-1&5&&-3&6-1&4&1&&1&38&1&-2&&4&1&&&&&-4&2&6&&9&1end{bmatrix}}}\u3092\u3001A, B, C, D \u3092\u30d6\u30ed\u30c3\u30af\u3068\u3059\u308b\u533a\u5206\u884c\u5217\u3068\u547c\u3076\u3002\u30d6\u30ed\u30c3\u30af\u306f\u5c0f\u884c\u5217\u3068\u3082\u547c\u3070\u308c\u308b\u3002\u884c\u5217\u3092\u30d6\u30ed\u30c3\u30af\u306b\u5206\u3051\u308b\u3053\u3068\u3092\u533a\u5206\u3051\u3068\u3044\u3046\u3002\u4e00\u822c\u306e\u533a\u5206\u3051\u3067\u306f\u3001\u884c\u3084\u5217\u3092\u305d\u308c\u305e\u308c\u3044\u304f\u3064\u306b\u5206\u5272\u3057\u3066\u3082\u3088\u3044\u3002Aij \u305f\u3061\u3092\u30d6\u30ed\u30c3\u30af\u3068\u3059\u308b\u533a\u5206\u884c\u5217  [A11A12\u22efA1qA21A22\u22efA2q\u22ee\u22ee\u22f1\u22eeAp1Ap2\u22efApq]{displaystyle {begin{bmatrix}A_{11}&A_{12}&cdots &A_{1q}A_{21}&A_{22}&cdots &A_{2q}vdots &vdots &ddots &vdots A_{p1}&A_{p2}&cdots &A_{pq}end{bmatrix}}}\u304c\u533a\u5206\u3051\u306e\u4e00\u822c\u7684\u306a\u5f62\u3067\u3042\u308b\u3002\u305f\u3060\u3057\u3001\u540c\u3058\u884c\u306b\u3042\u308b\u30d6\u30ed\u30c3\u30af\u306e\u884c\u6570\u306f\u7b49\u3057\u304f\u306a\u3051\u308c\u3070\u306a\u3089\u305a\u3001\u540c\u3058\u5217\u306b\u3042\u308b\u30d6\u30ed\u30c3\u30af\u306e\u5217\u6570\u306f\u7b49\u3057\u304f\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u3002Ai j \u304c mi \u00d7 nj \u884c\u5217\u3067\u3042\u308b\u5834\u5408\u3001\u3053\u306e\u5f62\u306e\u533a\u5206\u3051\u3092 (m1, \u2026, mq; n1, \u2026, nr) \u578b\u3068\u547c\u3076\u3002Table of Contents\u533a\u5206\u884c\u5217\u306e\u7a4d[\u7de8\u96c6]\u5bfe\u79f0\u533a\u5206\u3051[\u7de8\u96c6]2 \u00d7 2 \u306e\u533a\u5206\u884c\u5217\u306e\u9006\u884c\u5217[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u533a\u5206\u884c\u5217\u306e\u7a4d[\u7de8\u96c6]\u3075\u305f\u3064\u306e\u533a\u5206\u884c\u5217A=[A11A12\u22efA1qA21A22\u22efA2q\u22ee\u22ee\u22f1\u22eeAp1Ap2\u22efApq],B=[B11B12\u22efB1rB21B22\u22efB2r\u22ee\u22ee\u22f1\u22eeBq1Bq2\u22efBqr]{displaystyle A={begin{bmatrix}A_{11}&A_{12}&cdots &A_{1q}A_{21}&A_{22}&cdots &A_{2q}vdots &vdots &ddots &vdots A_{p1}&A_{p2}&cdots &A_{pq}end{bmatrix}},quad B={begin{bmatrix}B_{11}&B_{12}&cdots &B_{1r}B_{21}&B_{22}&cdots &B_{2r}vdots &vdots &ddots &vdots B_{q1}&B_{q2}&cdots &B_{qr}end{bmatrix}}}\u306e\u533a\u5206\u3051\u304c\u305d\u308c\u305e\u308c (l1, \u2026, lp; m1, \u2026, mq) \u578b\u3001(m1, \u2026, mq; n1, \u2026, nr) \u578b\u3067\u3042\u308b\u3068\u304d\u3001\u305d\u306e\u7a4d AB \u306e (l1, \u2026, lp; n1, \u2026, nr) \u578b\u306e\u533a\u5206\u3051AB=[C11C12\u22efC1rC21C22\u22efC2r\u22ee\u22ee\u22f1\u22eeCp1Cp2\u22efCpr]{displaystyle AB={begin{bmatrix}C_{11}&C_{12}&cdots &C_{1r}C_{21}&C_{22}&cdots &C_{2r}vdots &vdots &ddots &vdots C_{p1}&C_{p2}&cdots &C_{pr}end{bmatrix}}}\u306e\u5404\u30d6\u30ed\u30c3\u30af\u306fCij=\u2211k=1qAikBkj{displaystyle C_{ij}=sum _{k=1}^{q}A_{ik}B_{kj}}\u3067\u4e0e\u3048\u3089\u308c\u308b\u3002\u3059\u306a\u308f\u3061\u3001\u533a\u5206\u884c\u5217\u306e\u7a4d\u306f\uff08\u9069\u5207\u306b\u533a\u5206\u3051\u3055\u308c\u3066\u3044\u308c\u3070\uff09\u5404\u30d6\u30ed\u30c3\u30af\u3092\u3042\u305f\u304b\u3082\u884c\u5217\u306e\u6210\u5206\u306e\u3088\u3046\u306b\u898b\u306a\u3057\u3066\u8a08\u7b97\u3067\u304d\u308b\u3002\u5bfe\u79f0\u533a\u5206\u3051[\u7de8\u96c6]\u6b63\u65b9\u884c\u5217 P \u306e\u533a\u5206\u3051P=[A11A12\u2026A1rA21A22\u2026A2r\u22ee\u22ee\u22f1\u22eeAr1Ar2\u2026Arr]{displaystyle P={begin{bmatrix}A_{11}&A_{12}&dots &A_{1r}A_{21}&A_{22}&dots &A_{2r}vdots &vdots &ddots &vdots A_{r1}&A_{r2}&dots &A_{rr}end{bmatrix}}}\u306b\u304a\u3044\u3066\u3001\u4e3b\u5bfe\u89d2\u7dda\u4e0a\u306e\u30d6\u30ed\u30c3\u30af A1 1, A2 2, \u2026 Ar r \u304c\u3059\u3079\u3066\u6b63\u65b9\u884c\u5217\u3067\u3042\u308b\u3068\u304d\u3001\u3053\u308c\u3092\u5bfe\u79f0\u533a\u5206\u3051\u3068\u3044\u3046\u3002\u7279\u306b\u3001\u4e3b\u5bfe\u89d2\u7dda\u3088\u308a\u4e0b\u306e\u30d6\u30ed\u30c3\u30af\u304c\u5168\u3066\u96f6\u884c\u5217\u3067\u3042\u308b\u5834\u5408\u3001\u305d\u306e\u884c\u5217\u5f0f\u306b\u3064\u3044\u3066|P|=\u220fk=1r|Akk|{displaystyle |P|=prod _{k=1}^{r}|A_{kk}|}\u304c\u6210\u308a\u7acb\u3064\u3002\u3088\u3063\u3066\u3001\u305d\u306e\u3088\u3046\u306a P \u304c\u6b63\u5247\u3067\u3042\u308b\u305f\u3081\u306e\u5fc5\u8981\u5341\u5206\u6761\u4ef6\u306f\u3001\u4e3b\u5bfe\u89d2\u7dda\u4e0a\u306e\u30d6\u30ed\u30c3\u30af\u304c\u5168\u3066\u6b63\u5247\u3067\u3042\u308b\u3053\u3068\u3067\u3042\u308b\u30022 \u00d7 2 \u306e\u533a\u5206\u884c\u5217\u306e\u9006\u884c\u5217[\u7de8\u96c6]\u672c\u7bc0\u3067\u306f\u3001A \u306f\u6b63\u5247\u884c\u5217\u3001D \u306f\u6b63\u65b9\u884c\u5217\u3068\u3057\u3001\u533a\u5206\u884c\u5217P=[ABCD]{displaystyle P={begin{bmatrix}A&BC&Dend{bmatrix}}}\u306e\u9006\u884c\u5217\u3092\u4e0e\u3048\u308b\u3002\u307e\u305a\u3001\u884c\u5217\u5f0f\u306b\u3064\u3044\u3066\u3001|P|=|A||D\u2212CA\u22121B|{displaystyle |P|=|A||D-CA^{-1}B|,}\u304c\u6210\u308a\u7acb\u3064\u3002\u3088\u3063\u3066\u3001P \u304c\u6b63\u5247\u3067\u3042\u308b\u305f\u3081\u306e\u5fc5\u8981\u5341\u5206\u6761\u4ef6\u306f\u3001D \u2212 CA\u22121B \u3082\u6b63\u5247\u3067\u3042\u308b\u3053\u3068\u3067\u3042\u308a\u3001\u3053\u306e\u3068\u304d\u9006\u884c\u5217\u306f[ABCD]\u22121=[A\u22121+A\u22121B(D\u2212CA\u22121B)\u22121CA\u22121\u2212A\u22121B(D\u2212CA\u22121B)\u22121\u2212(D\u2212CA\u22121B)\u22121CA\u22121(D\u2212CA\u22121B)\u22121]{displaystyle {begin{bmatrix}A&BC&Dend{bmatrix}}^{-1}={begin{bmatrix}A^{-1}+A^{-1}B(D-CA^{-1}B)^{-1}CA^{-1}&-A^{-1}B(D-CA^{-1}B)^{-1}-(D-CA^{-1}B)^{-1}CA^{-1}&(D-CA^{-1}B)^{-1}end{bmatrix}}}\u3067\u4e0e\u3048\u3089\u308c\u308b\u3002D \u3082\u6b63\u5247\u306a\u5834\u5408\u306f[ABCD]\u22121=[(A\u2212BD\u22121C)\u22121\u2212A\u22121B(D\u2212CA\u22121B)\u22121\u2212(D\u2212CA\u22121B)\u22121CA\u22121(D\u2212CA\u22121B)\u22121]{displaystyle {begin{bmatrix}A&BC&Dend{bmatrix}}^{-1}={begin{bmatrix}(A-BD^{-1}C)^{-1}&-A^{-1}B(D-CA^{-1}B)^{-1}-(D-CA^{-1}B)^{-1}CA^{-1}&(D-CA^{-1}B)^{-1}end{bmatrix}}}\u3068\u8868\u3055\u308c\u308b\u3002\u3055\u3089\u306b C \u304c\u96f6\u884c\u5217 O \u306b\u7b49\u3057\u3044\u5834\u5408\u306f[ABOD]\u22121=[A\u22121\u2212A\u22121BD\u22121OD\u22121]{displaystyle {begin{bmatrix}A&BO&Dend{bmatrix}}^{-1}={begin{bmatrix}A^{-1}&-A^{-1}BD^{-1}O&D^{-1}end{bmatrix}}}\u3068\u306a\u308b\u3002\u53c2\u8003\u6587\u732e[\u7de8\u96c6]"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki6\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/10857#breadcrumbitem","name":"\u533a\u5206\u884c\u5217 – Wikipedia"}}]}]