{"id":5388,"date":"2014-04-18T06:00:24","date_gmt":"2014-04-17T21:00:24","guid":{"rendered":"http:\/\/fujiitoshiki.com\/improvesociety\/?p=5388"},"modified":"2014-09-10T16:36:01","modified_gmt":"2014-09-10T07:36:01","slug":"post-5388","status":"publish","type":"post","link":"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=5388","title":{"rendered":"\u3044\u304f\u3064\u304b\u306e\u884c\u5217\u3092\u542b\u3080\u7279\u6b8a\u306a\u5b9a\u7fa9\u3068\u6f14\u7b97"},"content":{"rendered":"

1. \u884c\u5217\u304c\u7b49\u3057\u3044<\/h4>\n
\u3000\u4e8c\u3064\u306e\u884c\u5217 $A = (a_{jk})$ \u304a\u3088\u3073 $B = (b_{jk})$ \u304c\u540c\u3058\u6b21\u6570\u3067\uff08\u3059\u306a\u308f\u3061\u884c\u3068\u5217\u306e\u6570\u304c\u540c\u3058\u3067\uff09 $a_{jk} = b_{jk}$ \u306e\u6642\u306b\u306e\u307f \u7b49\u3057\u3044<\/em>\uff0e<\/p>\n

2. \u884c\u5217\u306e\u548c<\/h4>\n
\u3000\u4eee\u306b $A = (a_{jk})$ \u304a\u3088\u3073 $B = (b_{jk})$ \u304c\u540c\u3058\u6b21\u6570\u306a\u3089\u3070 $A$ \u304a\u3088\u3073 $B$ \u306e \u548c<\/em> \u3092 $A + B = (a_{jk} + b_{jk})$ \u3068\u5b9a\u7fa9\u3067\u304d\u307e\u3059\uff0e<\/p>\n
\u3000\u884c\u5217\u306e\u4ea4\u63db\u6cd5\u5247\u3068\u7d50\u5408\u6cd5\u5247\u306f\uff0c\u3059\u306a\u308f\u3061\u3042\u308b\u540c\u3058\u6b21\u6570\u306e\u884c\u5217 $A,\\ B,\\ C$ \u3092\u4e0b\u8a18\u306e\u3088\u3046\u306b\u8a18\u8ff0\u3057\u307e\u3059\uff0e<\/p>\n
$A + B = B + A,\\ A + (B + C) = (A + B) + C \\cdots (2)$ <\/p>\n
3. \u884c\u5217\u306e\u5dee<\/h4>\n
\u3000\u4eee\u306b $A = (a_{jk})$ , $B = (b_{jk})$ \u304c\u540c\u3058\u6b21\u6570\u3092\u6709\u3059\u308b\u306a\u3089 $A$ \u304a\u3088\u3073 $B$ \u306e \u5dee<\/em> \u3092 $A - B = (a_{jk} - b_{jk})$ \u3068\u5b9a\u7fa9\u3067\u304d\u307e\u3059\uff0e<\/p>\n
4. \u884c\u5217\u306e\u30b9\u30ab\u30e9\u30fc\u500d<\/h4>\n
\u3000\u4eee\u306b $A = (a_{jk})$ \u304c\u3042\u3063\u3066 $\\lambda$ \u304c\u4efb\u610f\u306e\u6570\u307e\u305f\u306f\u30b9\u30ab\u30e9\u30fc\u306e\u6642 $A$ \u306e $\\lambda$ \u306b\u3088\u308b \u7a4d<\/em> \u3092 $\\lambda A = A\\lambda = (\\lambda a_{jk})$ \u3068\u5b9a\u7fa9\u3067\u304d\u307e\u3059\uff0e<\/p>\n
5. \u884c\u5217\u306e\u7a4d<\/h4>\n
\u3000\u4eee\u306b $A = (a_{jk})$ \u304c $m\\times n$ \u884c\u5217\u3067 $B = (b_{jk})$ \u304c $n\\times p$ \u884c\u5217\u306e\u6642\uff0c $A\\cdot B$ \u307e\u305f\u306f $AB$ \u306e \u7a4d<\/em> \u3092\u884c\u5217 $C = (c_{jk})$ \u3068\u5b9a\u7fa9\u3067\u304d\u307e\u3059\uff0e\u3053\u3053\u3067<\/p>\n
$\\displaystyle c_{jk} = \\sum_{l = 1}^n a_{jl}b_{lk} \\cdots (3)$ <\/p>\n
\u307e\u305f $C$ \u306f $m\\times p$ \u6b21\u3067\u3059\uff0e<\/p>\n
\u3000\u4e00\u822c\u306b $AB \\ne BA$ \u3059\u306a\u308f\u3061\u884c\u5217\u306e\u7a4d\u306e\u4ea4\u63db\u6cd5\u5247\u306f\u6210\u308a\u7acb\u305f\u306a\u3044\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\uff0e\u3057\u304b\u3057\u306a\u304c\u3089\u7d50\u5408\u6cd5\u5247\u3068\u5206\u914d\u6cd5\u5247\u306f\u6210\u308a\u7acb\u3061\u307e\u3059\uff0c\u3059\u306a\u308f\u3061<\/p>\n
$A(BC) = (AB)C,\\ A(B + C) = AB + AC,\\ (B + C)A = BA + CA \\cdots (4)$ <\/p>\n
\u3000\u3042\u308b\u884c\u5217 $A$ \u304c\u305d\u308c\u81ea\u8eab\u3068\u306e\u7a4d\u3092\u3064\u304f\u308c\u308b\u306e\u306f\u6b63\u65b9\u884c\u5217\u306e\u5834\u5408\u306e\u307f\u3067\u3059\uff0e\u7a4d $A \\cdot A$ \u306f $A^2$ \u3068\u8a18\u8ff0\u3057\u307e\u3059\uff0e\u540c\u69d8\u306b\u884c\u5217\u306e\u7d2f\u4e57\u3092\u5b9a\u7fa9\u3067\u304d\u307e\u3059\uff0e\u3059\u306a\u308f\u3061 $A^3 = A\\cdot A^2,\\ A^4 = A\\cdot A^3$ \u306a\u3069\u3067\u3059\uff0e<\/p>\n
6. \u884c\u5217\u306e\u8ee2\u7f6e<\/h4>\n
\u3000\u884c\u5217 $A$ \u306e\u884c\u3068\u5217\u3092\u5165\u308c\u66ff\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u306a\u3089\uff0c\u305d\u306e\u7d50\u679c\u5f97\u3089\u308c\u308b\u884c\u5217\u306f $A$ \u306e \u8ee2\u7f6e<\/em> \u3068\u547c\u3073\uff0c $A^T$ \u3068\u8a18\u8ff0\u3057\u307e\u3059\uff0e\u8a18\u53f7\u3067\u306f\uff0c\u4eee\u306b $A = (a_{jk})$ \u306a\u3089\u3070 $A^T = (a_{kj})$ \u3068\u8a18\u8ff0\u3057\u307e\u3059\uff0e<\/p>\n
\u4ee5\u4e0b\u3092\u8a3c\u660e\u3067\u304d\u307e\u3059\uff0e<\/p>\n
$(A + B)^T = A^T + B^T,\\ (AB)^T = B^TA^T,\\ (A^T)^T = A \\cdots(5)$ <\/p>\n
7. \u5bfe\u79f0\u884c\u5217\u3068\u6b6a\u5bfe\u79f0\u884c\u5217<\/h4>\n
\u3000\u3042\u308b\u6b63\u65b9\u884c\u5217 $A$ \u306f $A^T = A$ \u306e\u6642 \u5bfe\u79f0<\/em> \u3068\u547c\u3073\uff0c $A^T = - A$ \u306e\u6642 \u6b6a\u5bfe\u79f0<\/em> \u3068\u547c\u3073\u307e\u3059\uff0e<\/p>\n
\u3000\u4efb\u610f\u306e\u5b9f\u6b63\u65b9\u884c\u5217\uff08\u3059\u306a\u308f\u3061\u5b9f\u6570\u306e\u8981\u7d20\u306e\u307f\u304b\u3089\u306a\u308b\u5b9f\u6b63\u65b9\u884c\u5217\uff09\u306f\u5e38\u306b\u5b9f\u5bfe\u79f0\u884c\u5217\u3068\u5b9f\u6b6a\u5bfe\u79f0\u884c\u5217\u306e\u548c\u3067\u8868\u73fe\u3067\u304d\u307e\u3059\uff0e<\/p>\n
8. \u884c\u5217\u306e\u8907\u7d20\u5171\u5f79<\/h4>\n
\u3000\u4eee\u306b\u884c\u5217 $A$ \u306e\u3059\u3079\u3066\u306e\u8981\u7d20 $a_{jk}$ \u304c\u8907\u7d20\u5171\u5f79 $\\bar{a}_{jk}$ \u3067\u7f6e\u304d\u63db\u3048\u3089\u308c\u305f\u3089\uff0c\u305d\u306e\u7d50\u679c\u5f97\u3089\u308c\u305f\u884c\u5217\u306f $A$ \u306e \u8907\u7d20\u5171\u5f79<\/em> \u3068\u547c\u3073\uff0c $\\bar{A}$ \u3068\u8a18\u8ff0\u3057\u307e\u3059\uff0e<\/p>\n
9. \u30a8\u30eb\u30df\u30fc\u30c8\u884c\u5217\u53ca\u3073\u6b6a\u30a8\u30eb\u30df\u30fc\u30c8\u884c\u5217<\/h4>\n
\u3000\u3042\u308b\u884c\u5217 $A$ \u304c\u305d\u308c\u81ea\u8eab\u306e\u8ee2\u7f6e\u306e\u8907\u7d20\u5171\u5f79\u306b\u7b49\u3057\u3044\u6642\uff0c\u3059\u306a\u308f\u3061 $A = \\bar{A}^T$ \u3067\u3042\u308b\u306a\u3089 \u30a8\u30eb\u30df\u30fc\u30c8\u884c\u5217<\/em> \u3068\u547c\u3073\u307e\u3059\uff0e\u4eee\u306b $A = -\\bar{A}^T$ \u306e\u5834\u5408\u306f $A$ \u306f \u6b6a\u30a8\u30eb\u30df\u30fc\u30c8\u884c\u5217<\/em> \u3068\u547c\u3073\u307e\u3059\uff0e\u4eee\u306b $A$ \u304c\u5b9f\u884c\u5217\u306a\u3089\u3053\u308c\u3089\u306f\u5bfe\u79f0\u884c\u5217\u304a\u3088\u3073\u6b6a\u5bfe\u79f0\u884c\u5217\u306b\u305d\u308c\u305e\u308c\u77ed\u7e2e\u3055\u308c\u307e\u3059\uff0e<\/p>\n
10. \u4e3b\u5bfe\u89d2\u7dda\u3068\u884c\u5217\u306e\u30c8\u30ec\u30fc\u30b9<\/h4>\n
\u3000\u4eee\u306b $A = (a_{jk})$ \u3092\u6b63\u65b9\u884c\u5217\u3068\u3059\u308b\u3068\u5bfe\u89d2\u7dda\u4e0a\u306e\u3059\u3079\u3066\u306e\u8981\u7d20 $a_{jk}$ \u306b\u3064\u3044\u3066 $j = k$ \u3067\u3042\u308b\u3082\u306e\u3092 principal<\/em> \u3042\u308b\u3044\u306f \u4e3b\u5bfe\u89d2\u7dda<\/em> \u3068\u547c\u3073\uff0c\u4e3b\u5bfe\u89d2\u7dda\u4e0a\u306e\u5168\u8981\u7d20\u306e\u548c\u3092 $A$ \u306e \u30c8\u30ec\u30fc\u30b9<\/em> \u3068\u547c\u3073\u307e\u3059\uff0e<\/p>\n
\u3000\u3042\u308b\u884c\u5217\u306e $j \\ne k$ \u306a\u308b\u8981\u7d20\u306b\u3064\u3044\u3066 $a_{jk} = 0$ \u306e\u6642\u305d\u306e\u884c\u5217\u3092 \u5bfe\u89d2\u884c\u5217<\/em> \u3068\u547c\u3073\u307e\u3059\uff0e<\/p>\n
11. \u5358\u4f4d\u884c\u5217<\/h4>\n
\u3000\u3042\u308b\u6b63\u65b9\u884c\u5217\u306b\u3064\u3044\u3066\u4e3b\u5bfe\u89d2\u7dda\u4e0a\u306e\u5168\u8981\u7d20\u304c 1 \u306b\u7b49\u3057\u304f\u4ed6\u306e\u8981\u7d20\u304c\u5168\u3066\u30bc\u30ed\u306b\u7b49\u3057\u3044\u6642 \u5358\u4f4d\u884c\u5217<\/em> \u3068\u547c\u3073\uff0c $I$ \u3068\u8a18\u8ff0\u3057\u307e\u3059\uff0e $I$ \u306e\u5c5e\u6027\u306b\u3064\u3044\u3066\u306f\u975e\u5e38\u306b\u91cd\u8981\u3067\u3059\uff0e<\/p>\n
$AI = IA = A,\\ I^n = I,\\ n = 1,2,3,\\cdots(6)$ <\/p>\n
\u3000\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u306f\u884c\u5217\u4ee3\u6570\u306b\u304a\u3044\u3066\uff0c\u666e\u901a\u306e\u4ee3\u6570\u306b\u304a\u3051\u308b\u6570 1 \u3068\u540c\u3058\u5f79\u5272\u3092\u679c\u305f\u3057\u307e\u3059\uff0e<\/p>\n
12. \u96f6\u884c\u5217\u307e\u305f\u306f\u30cc\u30eb\u884c\u5217<\/h4>\n
\u3000\u3042\u308b\u884c\u5217\u306b\u3064\u3044\u3066\u305d\u306e\u8981\u7d20\u304c\u5168\u3066\u30bc\u30ed\u306b\u7b49\u3057\u3044\u306a\u3089 \u30cc\u30eb\u884c\u5217<\/em> \u307e\u305f\u306f \u96f6\u884c\u5217<\/em> \u3068\u547c\u3073\uff0c $O$ \u307e\u305f\u306f\u5358\u306b 0 \u3068\u8a18\u8ff0\u3057\u307e\u3059\uff0e\u3059\u3079\u3066\u306e\u884c\u5217 $A$ \u306b\u3064\u3044\u3066\u540c\u6b21\u6570\u306e 0 \u3092\u8003\u3048\u308b\u3068\uff0c<\/p>\n
$A + 0 = 0 + A = A \\cdots(7)$ <\/p>\n
\u3000\u307e\u305f\u4eee\u306b $A$ \u304a\u3088\u3073 0 \u304c\u6b63\u65b9\u884c\u5217\u306a\u3089<\/p>\n
$A0 = 0A = 0 \\cdots(8)$ <\/p>\n
\u3000\u96f6\u884c\u5217\u306f\u884c\u5217\u4ee3\u6570\u306b\u304a\u3044\u3066\u306f\u901a\u5e38\u306e\u5bfe\u6570\u306b\u304a\u3051\u308b\u6570 0 \u3068\u540c\u3058\u5f79\u5272\u3092\u679c\u305f\u3057\u307e\u3059\uff0e<\/p>\n
<\/iframe><\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>1. \u884c\u5217\u304c\u7b49\u3057\u3044 \u3000\u4e8c\u3064\u306e\u884c\u5217 \u304a\u3088\u3073 \u304c\u540c\u3058\u6b21\u6570\u3067\uff08\u3059\u306a\u308f\u3061\u884c\u3068\u5217\u306e\u6570\u304c\u540c\u3058\u3067\uff09 \u306e\u6642\u306b\u306e\u307f \u7b49\u3057\u3044\uff0e 2. \u884c\u5217\u306e\u548c \u3000\u4eee\u306b \u304a\u3088\u3073 \u304c\u540c\u3058\u6b21\u6570\u306a\u3089\u3070 \u304a\u3088\u3073 \u306e \u548c \u3092 \u3068\u5b9a\u7fa9\u3067\u304d\u307e\u3059\uff0e \u3000\u884c\u5217\u306e\u4ea4\u63db\u6cd5\u5247\u3068\u7d50\u5408\u6cd5 … <a href=\"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=5388\" class=\"more-link\"><span class=\"screen-reader-text\">“\u3044\u304f\u3064\u304b\u306e\u884c\u5217\u3092\u542b\u3080\u7279\u6b8a\u306a\u5b9a\u7fa9\u3068\u6f14\u7b97” \u306e<\/span>\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":1,"featured_media":6040,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[9],"tags":[],"class_list":["post-5388","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/5388","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5388"}],"version-history":[{"count":11,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/5388\/revisions"}],"predecessor-version":[{"id":6771,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/5388\/revisions\/6771"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/media\/6040"}],"wp:attachment":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5388"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5388"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5388"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}