Theo truy\u1ec1n thuy\u1ebft v\u00e0o th\u1eddi vua \u0110\u1ea1i V\u0169 tr\u1ecb thu\u1ef7 (23 th\u1ebf k\u1ec9 tr\u01b0\u1edbc C\u00f4ng Nguy\u00ean), c\u00f3 m\u1ed9t con r\u00f9a l\u1edbn n\u1ed5i l\u00ean tr\u00ean s\u00f4ng L\u1ea1c, tr\u00ean l\u01b0ng con r\u00f9a c\u00f3 ch\u00edn lo\u1ea1i hoa v\u0103n, ng\u01b0\u1eddi \u0111\u1eddi sau g\u1ecdi \u0111\u00f3 l\u00e0 \u201cL\u1ea1c th\u01b0\u201d. Tr\u00ean th\u1ef1c t\u1ebf \u0111\u00f3 l\u00e0 ch\u00edn s\u1ed1 t\u1ef1 nhi\u00ean li\u00ean t\u1ee5c \u0111\u01b0\u1ee3c x\u1ebfp tr\u00ean ba h\u00e0ng v\u1edbi ch\u00edn \u00f4. \u0110i\u1ec1u k\u00ec di\u1ec7u l\u00e0 \u1edf ch\u1ed7 t\u1ed5ng t\u1ea5t c\u1ea3 s\u1ed1 tr\u00ean m\u1ed9t h\u00e0ng ho\u1eb7c m\u1ed9t c\u1ed9t, tr\u00ean \u0111\u01b0\u1eddng ch\u00e9o \u0111\u1ec1u b\u1eb1ng 15, v\u1ea3 l\u1ea1i ch\u00edn s\u1ed1 t\u1ef1 nhi\u00ean n\u00e0y kh\u00f4ng c\u00f3 s\u1ef1 l\u1eb7p l\u1ea1i trong c\u00e1c \u00f4, c\u0169ng kh\u00f4ng b\u1ecf s\u00f3t.<\/p>\n\n\n\n
H\u01a1n n\u1eefa c\u00e1c nh\u00e0 nghi\u00ean c\u1ee9u l\u1ea1i th\u1ea5y l\u00e0 kh\u00f4ng ch\u1ec9 \u1edf L\u1ea1c th\u01b0 m\u1edbi c\u00f3 c\u00e1c \u00f4 vu\u00f4ng b\u00ed \u1ea9n n\u00e0y. N\u1ebfu x\u1ebfp c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean t\u1eeb 1 \u0111\u1ebfn n2 tr\u00ean c\u00e1c \u00f4 vu\u00f4ng th\u00ec ng\u01b0\u1eddi ta c\u0169ng thu \u0111\u01b0\u1ee3c c\u00e1c h\u00ecnh vu\u00f4ng c\u00f3 t\u00ednh ch\u1ea5t t\u01b0\u01a1ng t\u1ef1 v\u00e0 \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u201cbi\u1ec3u \u0111\u1ed3 ngang d\u1ecdc\u201d (\u0111\u1ed3 th\u1ecb 2 chi\u1ec1u), c\u00f2n \u1edf ph\u01b0\u01a1ng<\/p>\n\n\n\n
T\u00e2y ng\u01b0\u1eddi ta g\u1ecdi l\u00e0 \u201cma tr\u1eadn vu\u00f4ng \u1ea3o\u201d. C\u00e1c h\u00ecnh vu\u00f4ng c\u00f3 h\u00e0ng v\u00e0 c\u1ed9t v\u00e0 s\u1ed1 h\u00e0ng v\u00e0 c\u1ed9t l\u00e0 n th\u00ec g\u1ecdi l\u00e0 b\u1eadc c\u1ee7a h\u00ecnh vu\u00f4ng \u1ea3o hay \u201cma tr\u1eadn1 b\u1eadc n\u201d. B\u1eadc c\u1ee7a h\u00ecnh vu\u00f4ng trong \u201cL\u1ea1c th\u01b0\u201d l\u00e0 b\u1eadc ba (xem h\u00ecnh d\u01b0\u1edbi), \u0111\u00e2y ch\u00ednh l\u00e0 lo\u1ea1i ma tr\u1eadn \u0111\u01a1n gi\u1ea3n nh\u1ea5t.<\/p>\n\n\n\n
Ng\u01b0\u1eddi ta c\u00f2n t\u00ecm th\u1ea5y c\u00e1c s\u1ed1 trong ma tr\u1eadn ch\u1ec9 c\u1ea7n l\u00e0 n2 s\u1ed1 b\u1ea5t k\u00ec m\u00e0 kh\u00f4ng nh\u1ea5t thi\u1ebft ph\u1ea3i l\u00e0 c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean t\u1eeb 1 \u0111\u1ebfn n2. C\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean \u0111\u01b0\u1ee3c x\u1ebfp v\u00e0o c\u00e1c \u00f4 vu\u00f4ng g\u1ecdi l\u00e0 c\u00e1c ma tr\u1eadn c\u00f3 n c\u1ed9t, n h\u00e0ng.<\/p>\n\n\n\n
Ng\u00e0y nay c\u00e1c ma tr\u1eadn c\u00f3 b\u1eadc n ng\u00e0y c\u00e0ng l\u1edbn. Ma tr\u1eadn b\u1eadc ba hi\u1ec7n kh\u00f4ng ch\u1ec9 c\u00f3 m\u1ed9t ma tr\u1eadn trong L\u1ea1c th\u01b0. Xu\u1ea5t ph\u00e1t t\u1eeb ma tr\u1eadn L\u1ea1c th\u01b0 n\u1ebfu th\u00eam v\u00e0o c\u00e1c s\u1ed1 m\u1ed9t s\u1ed1, ta s\u1ebd \u0111\u01b0\u1ee3c m\u1ed9t ma tr\u1eadn m\u1edbi. V\u1edbi m\u1ed9t ma tr\u1eadn c\u1ea5p ba v\u1edbi m\u1ed9t s\u1ed1 k cho tr\u01b0\u1edbc n\u1ebfu th\u00eam v\u00e0o s\u1ed1 (k – 1)d (d l\u00e0 s\u1ed1 b\u1ea5t k\u00ec) ta c\u0169ng nh\u1eadn \u0111\u01b0\u1ee3c m\u1ed9t ma tr\u1eadn b\u1eadc ba m\u1edbi:<\/p>\n\n\n\n
C\u00e1c b\u1ea1n c\u00f3 th\u1ec3 t\u00ecm xem c\u00e1c ma tr\u1eadn n\u00e0y \u0111\u01b0\u1ee3c c\u1ea5u t\u1ea1o nh\u01b0 th\u1ebf n\u00e0o kh\u00f4ng?<\/p>\n\n\n\n
G\u1ea7n \u0111\u00e2y ng\u01b0\u1eddi ta \u0111\u00e3 m\u1edf r\u1ed9ng \u00fd ngh\u0129a c\u1ee7a ma tr\u1eadn. C\u00e1c ma tr\u1eadn n\u00e0y kh\u00f4ng ch\u1ec9 c\u00f3 t\u1ed5ng c\u00e1c s\u1ed1 theo h\u00e0ng ngang, h\u00e0ng d\u1ecdc, theo \u0111\u01b0\u1eddng ch\u00e9o b\u1eb1ng nhau m\u00e0 t\u00edch c\u00e1c s\u1ed1 c\u0169ng b\u1eb1ng nhau, ng\u01b0\u1eddi ta g\u1ecdi \u0111\u00f3 l\u00e0 c\u00e1c \u201cma tr\u1eadn k\u00e9p m\u1edf r\u1ed9ng\u201d. Hai ma tr\u1eadn k\u00e9p, m\u1ed9t ma tr\u1eadn c\u00f3 t\u00e1m h\u00e0ng, t\u00e1m c\u1ed9t, c\u00f2n ma tr\u1eadn kia c\u00f3 s\u1ed1 h\u00e0ng s\u1ed1 c\u1ed9t g\u1ea5p \u0111\u00f4i.<\/p>\n\n\n\n
Th\u1ebf li\u1ec7u c\u00e1c ma tr\u1eadn c\u00f3 \u1ee9ng d\u1ee5ng g\u00ec trong th\u1ef1c ti\u1ec5n? Tr\u01b0\u1edbc h\u1ebft ta th\u1eed xem lsy thuy\u1ebft \u201cthi \u0111\u1ea5u c\u1edd \u0111\u1ed3ng \u0111\u1ed9i\u201d. M\u1ecdi ng\u01b0\u1eddi \u0111\u1ec1u bi\u1ebft, trong thi \u0111\u1ea5u c\u1edd v\u00e2y, \u0111\u1ea5u th\u1ee7 \u1edf \u0111\u1eb3ng c\u1ea5p th\u1ea5p kh\u00f4ng th\u1ec3 th\u1eafng \u0111\u01b0\u1ee3c \u0111\u1ea5u th\u1ee7 \u0111\u1eb3ng c\u1ea5p cao h\u01a1n. Gi\u1ea3 s\u1eed tham d\u1ef1 thi \u0111\u1ea5u c\u1edd v\u00e2y c\u00f3 ba \u0111\u1ed9i A, B, C, m\u1ed7i \u0111\u1ed9i c\u00f3 ba k\u00ec th\u1ee7. Th\u1ef1c l\u1ef1c c\u1ee7a m\u1ed7i \u0111\u1ed9i c\u00f3 th\u1ec3 nh\u01b0 s\u1eafp x\u1ebfp \u1edf L\u1ea1c th\u01b0. \u0110\u1ed9i A c\u00f3 m\u1ed9t k\u00ec th\u1ee7 c\u1ea5p b\u1ed1n, c\u1ea5p ch\u00edn v\u00e0 c\u1ea5p hai; B c\u00f3 c\u00e1c k\u00ec th\u1ee7 \u1edf c\u00e1c \u0111\u1eb3ng c\u1ea5p c\u1ea5p ba, c\u1ea5p n\u0103m v\u00e0 c\u1ea5p b\u1ea3y; \u0110\u1ed9i C c\u00f3 c\u00e1c k\u00ec th\u1ee7 \u1edf c\u00e1c \u0111\u1eb3ng c\u1ea5p c\u1ea5p s\u00e1u, c\u1ea5p m\u1ed9t v\u00e0 c\u1ea5p s\u00e1u. N\u1ebfu c\u00e1c cu\u1ed9c thi \u0111\u1ea5u theo th\u1ec3 th\u1ee9c thi \u0111\u1ea5u v\u00f2ng tr\u00f2n th\u00ec c\u1ea7n ph\u1ea3i ti\u1ebfn h\u00e0nh ch\u00edn tr\u1eadn \u0111\u1ea5u m\u1edbi ph\u00e2n th\u1eafng b\u1ea1i. Ta th\u1eed xem x\u00e9t t\u00ecnh h\u00ecnh thi \u0111\u1ea5u c\u1ee7a hai \u0111\u1ed9i A v\u00e0 B. Theo nh\u01b0 c\u00e1ch s\u1eafp x\u1ebfp l\u1ef1c l\u01b0\u1ee3ng nh\u01b0 h\u00ecnh v\u1ebd, A c\u00f3 th\u1ec3 th\u1eafng b\u1ed1n tr\u1eadn c\u00f2n B c\u00f3 th\u1ec3 th\u1eafng n\u0103m tr\u1eadn v\u00e0 nh\u01b0 v\u1eady B > A. C\u0103n c\u1ee9 l\u00ed lu\u1eadn t\u01b0\u01a1ng t\u1ef1 ta th\u1ea5y C > B. Theo ti\u00ean \u0111\u1ec1 v\u1ec1 \u0111\u1ea1i l\u01b0\u1ee3ng kh\u00f4ng b\u1eb1ng nhau trong to\u00e1n h\u1ecdc ta c\u00f3 C > A. Th\u1ebf nh\u01b0ng ph\u00e2n t\u00edch theo L\u1ea1c th\u01b0 th\u00ec c\u0169ng d\u1ec5 th\u1ea5y C th\u1eafng b\u1ed1n tr\u1eadn c\u00f2n \u0111\u1ed9i A th\u1eafng n\u0103m tr\u1eadn v\u00e0 ta c\u00f3 A > C, v\u00ec v\u1eady \u1edf \u0111\u00e2y kh\u00f4ng th\u1ec3 \u1ee9ng d\u1ee5ng \u0111\u01b0\u1ee3c ti\u00ean \u0111\u1ec1 v\u1ec1 \u0111\u1ea1i l\u01b0\u1ee3ng kh\u00f4ng b\u1eb1ng nhau.<\/p>\n\n\n\n
V\u1edbi s\u1ef1 ph\u00e1t tri\u1ec3n c\u1ee7a m\u00e1y t\u00ednh \u0111i\u1ec7n t\u1eed, ma tr\u1eadn l\u1ea1i c\u00f3 th\u00eam m\u1ed9t \u00fd ngh\u0129a m\u1edbi. Tr\u01b0\u1edbc m\u1eaft, \u0111\u1ed1i v\u1edbi c\u00e1c m\u1eb7t ph\u00e2n t\u00edch t\u1ed5 h\u1ee3p, l\u00ed thuy\u1ebft \u0111\u1ed3 th\u1ecb, tr\u00ed tu\u1ec7 nh\u00e2n t\u1ea1o ma tr\u1eadn \u0111\u1ec1u c\u00f3 t\u00e1c d\u1ee5ng to l\u1edbn. Hi\u1ec7p h\u1ed9i m\u00e1y t\u00ednh M\u1ef9 khi so\u1ea1n th\u1ea3o tr\u1ee3 gi\u00fap tr\u1eadt t\u1ef1 b\u1ed9 nh\u1edb (CACM) \u0111\u00e3 so\u1ea1n th\u1ea3o vi\u1ec7c \u0111\u01b0a ma tr\u1eadn v\u00e0o vi\u1ec7c t\u1ea1o tr\u00ecnh t\u1ef1. Ki\u1ebfn tr\u00fac s\u01b0 B\u1ed9t La \u0110\u00f4ng \u0111\u00e3 ph\u00e1t hi\u1ec7n t\u00ednh \u0111\u1ed1i x\u1ee9ng h\u1ebft s\u1ee9c phong ph\u00fa c\u1ee7a c\u00e1c ma tr\u1eadn, trong \u0111\u00f3 c\u00f3 nhi\u1ec1u \u0111\u1ed3 \u00e1n r\u1ea5t \u0111\u1eb9p, c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng v\u00e0o c\u00e1c ng\u00e0nh c\u00f4ng nghi\u1ec7p nh\u1eb9, trong thi\u1ebft k\u1ebf<\/a> c\u00e1c bao b\u00ec.<\/p>\n\n\n\n Ma tr\u1eadn ng\u00e0y c\u00e0ng \u0111\u01b0\u1ee3c ng\u01b0\u1eddi ta coi tr\u1ecdng. \u1ede n\u01b0\u1edbc ngo\u00e0i \u0111\u00e3 xu\u1ea5t b\u1ea3n m\u1ed9t cu\u1ed1n s\u00e1ch n\u1ed5i ti\u1ebfng l\u00e0 \u201c\u0110\u1ea1i s\u1ed1 h\u1ecdc hi\u1ec7n \u0111\u1ea1i v\u00e0 \u1ee9ng d\u1ee5ng\u201d cu\u1ed1n s\u00e1ch \u0111\u00e3 m\u1edf ra l\u0129nh v\u1ef1c chuy\u00ean m\u00f4n m\u00e0 tr\u01b0\u1edbc \u0111\u00e2y ng\u01b0\u1eddi ta cho l\u00e0 tr\u00f2 t\u1ec9a t\u00f3t v\u00f4 b\u1ed5.<\/p>\n\n\n\n T\u1eeb kho\u00e1: H\u00ecnh vu\u00f4ng \u1ea3o; \u0110\u1ed3 th\u1ecb hai chi\u1ec1u..<\/p>\n\n\n\n <\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":" Theo truy\u1ec1n thuy\u1ebft v\u00e0o th\u1eddi vua \u0110\u1ea1i V\u0169 tr\u1ecb thu\u1ef7 (23 th\u1ebf k\u1ec9 tr\u01b0\u1edbc C\u00f4ng Nguy\u00ean), c\u00f3 m\u1ed9t con r\u00f9a l\u1edbn n\u1ed5i l\u00ean tr\u00ean s\u00f4ng L\u1ea1c, tr\u00ean l\u01b0ng con r\u00f9a c\u00f3 ch\u00edn lo\u1ea1i hoa v\u0103n, ng\u01b0\u1eddi \u0111\u1eddi sau g\u1ecdi \u0111\u00f3 l\u00e0 \u201cL\u1ea1c th\u01b0\u201d. Tr\u00ean th\u1ef1c t\u1ebf \u0111\u00f3 l\u00e0 ch\u00edn s\u1ed1 t\u1ef1 nhi\u00ean li\u00ean t\u1ee5c \u0111\u01b0\u1ee3c […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_disable_autopaging":false},"categories":[15,9],"tags":[],"class_list":["post-7585","post","type-post","status-publish","format-standard","hentry","category-hoi-dap-khoa-hoc","category-toan-hoc"],"_links":{"self":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7585","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/comments?post=7585"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7585\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=7585"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=7585"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=7585"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}